37:I[651451,["/_next/static/chunks/2msykuvi-vydm.js?dpl=nogit-1790362613","/_next/static/chunks/2mu6-wo6ccpi3.js?dpl=nogit-1790362613","/_next/static/chunks/2epfhfe5im7r6.js?dpl=nogit-1790362613","/_next/static/chunks/1ew75_i487l-5.js?dpl=nogit-1790362613","/_next/static/chunks/0p4rexedanx97.js?dpl=nogit-1790362613","/_next/static/chunks/0u008gt6051u7.js?dpl=nogit-1790362613","/_next/static/chunks/1odwrcl12kfnl.js?dpl=nogit-1790362613","/_next/static/chunks/0zkcxwtbsqliz.js?dpl=nogit-1790362613","/_next/static/chunks/3lf9kdvvybemj.js?dpl=nogit-1790362613","/_next/static/chunks/2hyw6fyf3iqeh.js?dpl=nogit-1790362613","/_next/static/chunks/03q735zs9dbpu.js?dpl=nogit-1790362613","/_next/static/chunks/3r5hh4t0jf4es.js?dpl=nogit-1790362613","/_next/static/chunks/3ml3vooxhiupb.js?dpl=nogit-1790362613","/_next/static/chunks/1h4wccj42vygd.js?dpl=nogit-1790362613","/_next/static/chunks/12xoy6h_w_le6.js?dpl=nogit-1790362613","/_next/static/chunks/2os7nxouq91eq.js?dpl=nogit-1790362613","/_next/static/chunks/3ht89vb0p09bm.js?dpl=nogit-1790362613","/_next/static/chunks/3ocoqwe4aht_u.js?dpl=nogit-1790362613","/_next/static/chunks/32qmkt01ta8b2.js?dpl=nogit-1790362613","/_next/static/chunks/3jpl-42mbad5n.js?dpl=nogit-1790362613","/_next/static/chunks/3ao1re0xmmur_.js?dpl=nogit-1790362613","/_next/static/chunks/3xa2z7fbv2riw.js?dpl=nogit-1790362613","/_next/static/chunks/14kf-an-d2n-e.js?dpl=nogit-1790362613","/_next/static/chunks/381o-754ev9ia.js?dpl=nogit-1790362613","/_next/static/chunks/2tr2cll18vqv3.js?dpl=nogit-1790362613","/_next/static/chunks/0v4byuex1x38h.js?dpl=nogit-1790362613","/_next/static/chunks/3kom3ps_bn2q6.js?dpl=nogit-1790362613","/_next/static/chunks/1x_yxljsdq0vl.js?dpl=nogit-1790362613","/_next/static/chunks/1xkpwfqqdrdio.js?dpl=nogit-1790362613","/_next/static/chunks/04zr-wqafvwoa.js?dpl=nogit-1790362613","/_next/static/chunks/2dx-vzwyw9a3g.js?dpl=nogit-1790362613","/_next/static/chunks/2mv9l1xl_aa4j.js?dpl=nogit-1790362613","/_next/static/chunks/1ku-vdy4ggo41.js?dpl=nogit-1790362613","/_next/static/chunks/0k-y_4mcfub-p.js?dpl=nogit-1790362613","/_next/static/chunks/440m38krgocdi.js?dpl=nogit-1790362613","/_next/static/chunks/2p6gbbs6zvfpy.js?dpl=nogit-1790362613","/_next/static/chunks/172wsar4r7zzx.js?dpl=nogit-1790362613","/_next/static/chunks/0llqhg6-bxn_b.js?dpl=nogit-1790362613","/_next/static/chunks/1rbw_-uux6mpq.js?dpl=nogit-1790362613","/_next/static/chunks/1s6j_7_p0ugo9.js?dpl=nogit-1790362613","/_next/static/chunks/34ux0fo6f-rm8.js?dpl=nogit-1790362613","/_next/static/chunks/1pp_uf_jx5j9r.js?dpl=nogit-1790362613","/_next/static/chunks/2b6r02yb2zswo.js?dpl=nogit-1790362613","/_next/static/chunks/422ba61wql3d7.js?dpl=nogit-1790362613","/_next/static/chunks/2vg15qyptj-oc.js?dpl=nogit-1790362613","/_next/static/chunks/0d2u5k628p_lw.js?dpl=nogit-1790362613","/_next/static/chunks/3jzaxe43n3e1e.js?dpl=nogit-1790362613","/_next/static/chunks/1lsxkfxy262n-.js?dpl=nogit-1790362613","/_next/static/chunks/02e_f03j5ij1l.js?dpl=nogit-1790362613","/_next/static/chunks/12mv6p8rwcl5o.js?dpl=nogit-1790362613","/_next/static/chunks/0v5zhouho0zlq.js?dpl=nogit-1790362613","/_next/static/chunks/41x40gd5jiq0g.js?dpl=nogit-1790362613","/_next/static/chunks/2nnmvgmq4euk9.js?dpl=nogit-1790362613","/_next/static/chunks/1ksyn9m68446d.js?dpl=nogit-1790362613","/_next/static/chunks/3wqp-h5xnebw9.js?dpl=nogit-1790362613","/_next/static/chunks/30dopbgd1dkf9.js?dpl=nogit-1790362613","/_next/static/chunks/22z8pa0ys3w4l.js?dpl=nogit-1790362613","/_next/static/chunks/0zg1om_k0m5zv.js?dpl=nogit-1790362613","/_next/static/chunks/2ywf8cxod8dkv.js?dpl=nogit-1790362613","/_next/static/chunks/43ajf4ofaeu5y.js?dpl=nogit-1790362613","/_next/static/chunks/1__39-dgg7p8-.js?dpl=nogit-1790362613","/_next/static/chunks/1zt4k83kx3bkw.js?dpl=nogit-1790362613","/_next/static/chunks/0rt2_go1it43r.js?dpl=nogit-1790362613","/_next/static/chunks/200x0be4hbjpj.js?dpl=nogit-1790362613","/_next/static/chunks/35bn8r0ao86_s.js?dpl=nogit-1790362613","/_next/static/chunks/3xskuweujaw05.js?dpl=nogit-1790362613","/_next/static/chunks/2wlqtkfegn9hx.js?dpl=nogit-1790362613","/_next/static/chunks/2y341-r8ncizo.js?dpl=nogit-1790362613","/_next/static/chunks/03ai9i_h50rnc.js?dpl=nogit-1790362613","/_next/static/chunks/0pdzmybpnr872.js?dpl=nogit-1790362613"],"UserProgressProvider"] 38:I[196793,["/_next/static/chunks/2msykuvi-vydm.js?dpl=nogit-1790362613","/_next/static/chunks/2mu6-wo6ccpi3.js?dpl=nogit-1790362613","/_next/static/chunks/2epfhfe5im7r6.js?dpl=nogit-1790362613","/_next/static/chunks/1ew75_i487l-5.js?dpl=nogit-1790362613","/_next/static/chunks/0p4rexedanx97.js?dpl=nogit-1790362613","/_next/static/chunks/0u008gt6051u7.js?dpl=nogit-1790362613","/_next/static/chunks/1odwrcl12kfnl.js?dpl=nogit-1790362613","/_next/static/chunks/0zkcxwtbsqliz.js?dpl=nogit-1790362613","/_next/static/chunks/3lf9kdvvybemj.js?dpl=nogit-1790362613","/_next/static/chunks/2hyw6fyf3iqeh.js?dpl=nogit-1790362613","/_next/static/chunks/03q735zs9dbpu.js?dpl=nogit-1790362613","/_next/static/chunks/3r5hh4t0jf4es.js?dpl=nogit-1790362613","/_next/static/chunks/3ml3vooxhiupb.js?dpl=nogit-1790362613","/_next/static/chunks/1h4wccj42vygd.js?dpl=nogit-1790362613","/_next/static/chunks/12xoy6h_w_le6.js?dpl=nogit-1790362613","/_next/static/chunks/2os7nxouq91eq.js?dpl=nogit-1790362613","/_next/static/chunks/3ht89vb0p09bm.js?dpl=nogit-1790362613","/_next/static/chunks/3ocoqwe4aht_u.js?dpl=nogit-1790362613","/_next/static/chunks/32qmkt01ta8b2.js?dpl=nogit-1790362613","/_next/static/chunks/3jpl-42mbad5n.js?dpl=nogit-1790362613","/_next/static/chunks/3ao1re0xmmur_.js?dpl=nogit-1790362613","/_next/static/chunks/3xa2z7fbv2riw.js?dpl=nogit-1790362613","/_next/static/chunks/14kf-an-d2n-e.js?dpl=nogit-1790362613","/_next/static/chunks/381o-754ev9ia.js?dpl=nogit-1790362613","/_next/static/chunks/2tr2cll18vqv3.js?dpl=nogit-1790362613","/_next/static/chunks/0v4byuex1x38h.js?dpl=nogit-1790362613","/_next/static/chunks/3kom3ps_bn2q6.js?dpl=nogit-1790362613","/_next/static/chunks/1x_yxljsdq0vl.js?dpl=nogit-1790362613","/_next/static/chunks/1xkpwfqqdrdio.js?dpl=nogit-1790362613","/_next/static/chunks/04zr-wqafvwoa.js?dpl=nogit-1790362613","/_next/static/chunks/2dx-vzwyw9a3g.js?dpl=nogit-1790362613","/_next/static/chunks/2mv9l1xl_aa4j.js?dpl=nogit-1790362613","/_next/static/chunks/1ku-vdy4ggo41.js?dpl=nogit-1790362613","/_next/static/chunks/0k-y_4mcfub-p.js?dpl=nogit-1790362613","/_next/static/chunks/440m38krgocdi.js?dpl=nogit-1790362613","/_next/static/chunks/2p6gbbs6zvfpy.js?dpl=nogit-1790362613","/_next/static/chunks/172wsar4r7zzx.js?dpl=nogit-1790362613","/_next/static/chunks/0llqhg6-bxn_b.js?dpl=nogit-1790362613","/_next/static/chunks/1rbw_-uux6mpq.js?dpl=nogit-1790362613","/_next/static/chunks/1s6j_7_p0ugo9.js?dpl=nogit-1790362613","/_next/static/chunks/34ux0fo6f-rm8.js?dpl=nogit-1790362613","/_next/static/chunks/1pp_uf_jx5j9r.js?dpl=nogit-1790362613","/_next/static/chunks/2b6r02yb2zswo.js?dpl=nogit-1790362613","/_next/static/chunks/422ba61wql3d7.js?dpl=nogit-1790362613","/_next/static/chunks/2vg15qyptj-oc.js?dpl=nogit-1790362613","/_next/static/chunks/0d2u5k628p_lw.js?dpl=nogit-1790362613","/_next/static/chunks/3jzaxe43n3e1e.js?dpl=nogit-1790362613","/_next/static/chunks/1lsxkfxy262n-.js?dpl=nogit-1790362613","/_next/static/chunks/02e_f03j5ij1l.js?dpl=nogit-1790362613","/_next/static/chunks/12mv6p8rwcl5o.js?dpl=nogit-1790362613","/_next/static/chunks/0v5zhouho0zlq.js?dpl=nogit-1790362613","/_next/static/chunks/41x40gd5jiq0g.js?dpl=nogit-1790362613","/_next/static/chunks/2nnmvgmq4euk9.js?dpl=nogit-1790362613","/_next/static/chunks/1ksyn9m68446d.js?dpl=nogit-1790362613","/_next/static/chunks/3wqp-h5xnebw9.js?dpl=nogit-1790362613","/_next/static/chunks/30dopbgd1dkf9.js?dpl=nogit-1790362613","/_next/static/chunks/22z8pa0ys3w4l.js?dpl=nogit-1790362613","/_next/static/chunks/0zg1om_k0m5zv.js?dpl=nogit-1790362613","/_next/static/chunks/2ywf8cxod8dkv.js?dpl=nogit-1790362613","/_next/static/chunks/43ajf4ofaeu5y.js?dpl=nogit-1790362613","/_next/static/chunks/1__39-dgg7p8-.js?dpl=nogit-1790362613","/_next/static/chunks/1zt4k83kx3bkw.js?dpl=nogit-1790362613","/_next/static/chunks/0rt2_go1it43r.js?dpl=nogit-1790362613","/_next/static/chunks/200x0be4hbjpj.js?dpl=nogit-1790362613","/_next/static/chunks/35bn8r0ao86_s.js?dpl=nogit-1790362613","/_next/static/chunks/3xskuweujaw05.js?dpl=nogit-1790362613","/_next/static/chunks/2wlqtkfegn9hx.js?dpl=nogit-1790362613","/_next/static/chunks/2y341-r8ncizo.js?dpl=nogit-1790362613","/_next/static/chunks/03ai9i_h50rnc.js?dpl=nogit-1790362613","/_next/static/chunks/0pdzmybpnr872.js?dpl=nogit-1790362613"],"Gingerbread"] 3a:I[716297,["/_next/static/chunks/2msykuvi-vydm.js?dpl=nogit-1790362613","/_next/static/chunks/2mu6-wo6ccpi3.js?dpl=nogit-1790362613","/_next/static/chunks/2epfhfe5im7r6.js?dpl=nogit-1790362613","/_next/static/chunks/1ew75_i487l-5.js?dpl=nogit-1790362613","/_next/static/chunks/0p4rexedanx97.js?dpl=nogit-1790362613","/_next/static/chunks/0u008gt6051u7.js?dpl=nogit-1790362613","/_next/static/chunks/1odwrcl12kfnl.js?dpl=nogit-1790362613","/_next/static/chunks/0zkcxwtbsqliz.js?dpl=nogit-1790362613","/_next/static/chunks/3lf9kdvvybemj.js?dpl=nogit-1790362613","/_next/static/chunks/2hyw6fyf3iqeh.js?dpl=nogit-1790362613","/_next/static/chunks/03q735zs9dbpu.js?dpl=nogit-1790362613","/_next/static/chunks/3r5hh4t0jf4es.js?dpl=nogit-1790362613","/_next/static/chunks/3ml3vooxhiupb.js?dpl=nogit-1790362613","/_next/static/chunks/1h4wccj42vygd.js?dpl=nogit-1790362613","/_next/static/chunks/12xoy6h_w_le6.js?dpl=nogit-1790362613","/_next/static/chunks/2os7nxouq91eq.js?dpl=nogit-1790362613","/_next/static/chunks/3ht89vb0p09bm.js?dpl=nogit-1790362613","/_next/static/chunks/3ocoqwe4aht_u.js?dpl=nogit-1790362613","/_next/static/chunks/32qmkt01ta8b2.js?dpl=nogit-1790362613","/_next/static/chunks/3jpl-42mbad5n.js?dpl=nogit-1790362613","/_next/static/chunks/3ao1re0xmmur_.js?dpl=nogit-1790362613","/_next/static/chunks/3xa2z7fbv2riw.js?dpl=nogit-1790362613","/_next/static/chunks/14kf-an-d2n-e.js?dpl=nogit-1790362613","/_next/static/chunks/381o-754ev9ia.js?dpl=nogit-1790362613","/_next/static/chunks/2tr2cll18vqv3.js?dpl=nogit-1790362613","/_next/static/chunks/0v4byuex1x38h.js?dpl=nogit-1790362613","/_next/static/chunks/3kom3ps_bn2q6.js?dpl=nogit-1790362613","/_next/static/chunks/1x_yxljsdq0vl.js?dpl=nogit-1790362613","/_next/static/chunks/1xkpwfqqdrdio.js?dpl=nogit-1790362613","/_next/static/chunks/04zr-wqafvwoa.js?dpl=nogit-1790362613","/_next/static/chunks/2dx-vzwyw9a3g.js?dpl=nogit-1790362613","/_next/static/chunks/2mv9l1xl_aa4j.js?dpl=nogit-1790362613","/_next/static/chunks/1ku-vdy4ggo41.js?dpl=nogit-1790362613","/_next/static/chunks/0k-y_4mcfub-p.js?dpl=nogit-1790362613","/_next/static/chunks/440m38krgocdi.js?dpl=nogit-1790362613","/_next/static/chunks/2p6gbbs6zvfpy.js?dpl=nogit-1790362613","/_next/static/chunks/172wsar4r7zzx.js?dpl=nogit-1790362613","/_next/static/chunks/0llqhg6-bxn_b.js?dpl=nogit-1790362613","/_next/static/chunks/1rbw_-uux6mpq.js?dpl=nogit-1790362613","/_next/static/chunks/1s6j_7_p0ugo9.js?dpl=nogit-1790362613","/_next/static/chunks/34ux0fo6f-rm8.js?dpl=nogit-1790362613","/_next/static/chunks/1pp_uf_jx5j9r.js?dpl=nogit-1790362613","/_next/static/chunks/2b6r02yb2zswo.js?dpl=nogit-1790362613","/_next/static/chunks/422ba61wql3d7.js?dpl=nogit-1790362613","/_next/static/chunks/2vg15qyptj-oc.js?dpl=nogit-1790362613","/_next/static/chunks/0d2u5k628p_lw.js?dpl=nogit-1790362613","/_next/static/chunks/3jzaxe43n3e1e.js?dpl=nogit-1790362613","/_next/static/chunks/1lsxkfxy262n-.js?dpl=nogit-1790362613","/_next/static/chunks/02e_f03j5ij1l.js?dpl=nogit-1790362613","/_next/static/chunks/12mv6p8rwcl5o.js?dpl=nogit-1790362613","/_next/static/chunks/0v5zhouho0zlq.js?dpl=nogit-1790362613","/_next/static/chunks/41x40gd5jiq0g.js?dpl=nogit-1790362613","/_next/static/chunks/2nnmvgmq4euk9.js?dpl=nogit-1790362613","/_next/static/chunks/1ksyn9m68446d.js?dpl=nogit-1790362613","/_next/static/chunks/3wqp-h5xnebw9.js?dpl=nogit-1790362613","/_next/static/chunks/30dopbgd1dkf9.js?dpl=nogit-1790362613","/_next/static/chunks/22z8pa0ys3w4l.js?dpl=nogit-1790362613","/_next/static/chunks/0zg1om_k0m5zv.js?dpl=nogit-1790362613","/_next/static/chunks/2ywf8cxod8dkv.js?dpl=nogit-1790362613","/_next/static/chunks/43ajf4ofaeu5y.js?dpl=nogit-1790362613","/_next/static/chunks/1__39-dgg7p8-.js?dpl=nogit-1790362613","/_next/static/chunks/1zt4k83kx3bkw.js?dpl=nogit-1790362613","/_next/static/chunks/0rt2_go1it43r.js?dpl=nogit-1790362613","/_next/static/chunks/200x0be4hbjpj.js?dpl=nogit-1790362613","/_next/static/chunks/35bn8r0ao86_s.js?dpl=nogit-1790362613","/_next/static/chunks/3xskuweujaw05.js?dpl=nogit-1790362613","/_next/static/chunks/2wlqtkfegn9hx.js?dpl=nogit-1790362613","/_next/static/chunks/2y341-r8ncizo.js?dpl=nogit-1790362613","/_next/static/chunks/03ai9i_h50rnc.js?dpl=nogit-1790362613","/_next/static/chunks/0pdzmybpnr872.js?dpl=nogit-1790362613"],"TopicRecentlyViewed"] 3b:I[647935,["/_next/static/chunks/2msykuvi-vydm.js?dpl=nogit-1790362613","/_next/static/chunks/2mu6-wo6ccpi3.js?dpl=nogit-1790362613","/_next/static/chunks/2epfhfe5im7r6.js?dpl=nogit-1790362613","/_next/static/chunks/1ew75_i487l-5.js?dpl=nogit-1790362613","/_next/static/chunks/0p4rexedanx97.js?dpl=nogit-1790362613","/_next/static/chunks/0u008gt6051u7.js?dpl=nogit-1790362613","/_next/static/chunks/1odwrcl12kfnl.js?dpl=nogit-1790362613","/_next/static/chunks/0zkcxwtbsqliz.js?dpl=nogit-1790362613","/_next/static/chunks/3lf9kdvvybemj.js?dpl=nogit-1790362613","/_next/static/chunks/2hyw6fyf3iqeh.js?dpl=nogit-1790362613","/_next/static/chunks/03q735zs9dbpu.js?dpl=nogit-1790362613","/_next/static/chunks/3r5hh4t0jf4es.js?dpl=nogit-1790362613","/_next/static/chunks/3ml3vooxhiupb.js?dpl=nogit-1790362613","/_next/static/chunks/1h4wccj42vygd.js?dpl=nogit-1790362613","/_next/static/chunks/12xoy6h_w_le6.js?dpl=nogit-1790362613","/_next/static/chunks/2os7nxouq91eq.js?dpl=nogit-1790362613","/_next/static/chunks/3ht89vb0p09bm.js?dpl=nogit-1790362613","/_next/static/chunks/3ocoqwe4aht_u.js?dpl=nogit-1790362613","/_next/static/chunks/32qmkt01ta8b2.js?dpl=nogit-1790362613","/_next/static/chunks/3jpl-42mbad5n.js?dpl=nogit-1790362613","/_next/static/chunks/3ao1re0xmmur_.js?dpl=nogit-1790362613","/_next/static/chunks/3xa2z7fbv2riw.js?dpl=nogit-1790362613","/_next/static/chunks/14kf-an-d2n-e.js?dpl=nogit-1790362613","/_next/static/chunks/381o-754ev9ia.js?dpl=nogit-1790362613","/_next/static/chunks/2tr2cll18vqv3.js?dpl=nogit-1790362613","/_next/static/chunks/0v4byuex1x38h.js?dpl=nogit-1790362613","/_next/static/chunks/3kom3ps_bn2q6.js?dpl=nogit-1790362613","/_next/static/chunks/1x_yxljsdq0vl.js?dpl=nogit-1790362613","/_next/static/chunks/1xkpwfqqdrdio.js?dpl=nogit-1790362613","/_next/static/chunks/04zr-wqafvwoa.js?dpl=nogit-1790362613","/_next/static/chunks/2dx-vzwyw9a3g.js?dpl=nogit-1790362613","/_next/static/chunks/2mv9l1xl_aa4j.js?dpl=nogit-1790362613","/_next/static/chunks/1ku-vdy4ggo41.js?dpl=nogit-1790362613","/_next/static/chunks/0k-y_4mcfub-p.js?dpl=nogit-1790362613","/_next/static/chunks/440m38krgocdi.js?dpl=nogit-1790362613","/_next/static/chunks/2p6gbbs6zvfpy.js?dpl=nogit-1790362613","/_next/static/chunks/172wsar4r7zzx.js?dpl=nogit-1790362613","/_next/static/chunks/0llqhg6-bxn_b.js?dpl=nogit-1790362613","/_next/static/chunks/1rbw_-uux6mpq.js?dpl=nogit-1790362613","/_next/static/chunks/1s6j_7_p0ugo9.js?dpl=nogit-1790362613","/_next/static/chunks/34ux0fo6f-rm8.js?dpl=nogit-1790362613","/_next/static/chunks/1pp_uf_jx5j9r.js?dpl=nogit-1790362613","/_next/static/chunks/2b6r02yb2zswo.js?dpl=nogit-1790362613","/_next/static/chunks/422ba61wql3d7.js?dpl=nogit-1790362613","/_next/static/chunks/2vg15qyptj-oc.js?dpl=nogit-1790362613","/_next/static/chunks/0d2u5k628p_lw.js?dpl=nogit-1790362613","/_next/static/chunks/3jzaxe43n3e1e.js?dpl=nogit-1790362613","/_next/static/chunks/1lsxkfxy262n-.js?dpl=nogit-1790362613","/_next/static/chunks/02e_f03j5ij1l.js?dpl=nogit-1790362613","/_next/static/chunks/12mv6p8rwcl5o.js?dpl=nogit-1790362613","/_next/static/chunks/0v5zhouho0zlq.js?dpl=nogit-1790362613","/_next/static/chunks/41x40gd5jiq0g.js?dpl=nogit-1790362613","/_next/static/chunks/2nnmvgmq4euk9.js?dpl=nogit-1790362613","/_next/static/chunks/1ksyn9m68446d.js?dpl=nogit-1790362613","/_next/static/chunks/3wqp-h5xnebw9.js?dpl=nogit-1790362613","/_next/static/chunks/30dopbgd1dkf9.js?dpl=nogit-1790362613","/_next/static/chunks/22z8pa0ys3w4l.js?dpl=nogit-1790362613","/_next/static/chunks/0zg1om_k0m5zv.js?dpl=nogit-1790362613","/_next/static/chunks/2ywf8cxod8dkv.js?dpl=nogit-1790362613","/_next/static/chunks/43ajf4ofaeu5y.js?dpl=nogit-1790362613","/_next/static/chunks/1__39-dgg7p8-.js?dpl=nogit-1790362613","/_next/static/chunks/1zt4k83kx3bkw.js?dpl=nogit-1790362613","/_next/static/chunks/0rt2_go1it43r.js?dpl=nogit-1790362613","/_next/static/chunks/200x0be4hbjpj.js?dpl=nogit-1790362613","/_next/static/chunks/35bn8r0ao86_s.js?dpl=nogit-1790362613","/_next/static/chunks/3xskuweujaw05.js?dpl=nogit-1790362613","/_next/static/chunks/2wlqtkfegn9hx.js?dpl=nogit-1790362613","/_next/static/chunks/2y341-r8ncizo.js?dpl=nogit-1790362613","/_next/static/chunks/03ai9i_h50rnc.js?dpl=nogit-1790362613","/_next/static/chunks/0pdzmybpnr872.js?dpl=nogit-1790362613"],"RecordResourceResume"] 3c:I[426249,["/_next/static/chunks/2msykuvi-vydm.js?dpl=nogit-1790362613","/_next/static/chunks/2mu6-wo6ccpi3.js?dpl=nogit-1790362613","/_next/static/chunks/2epfhfe5im7r6.js?dpl=nogit-1790362613","/_next/static/chunks/1ew75_i487l-5.js?dpl=nogit-1790362613","/_next/static/chunks/0p4rexedanx97.js?dpl=nogit-1790362613","/_next/static/chunks/0u008gt6051u7.js?dpl=nogit-1790362613","/_next/static/chunks/1odwrcl12kfnl.js?dpl=nogit-1790362613","/_next/static/chunks/0zkcxwtbsqliz.js?dpl=nogit-1790362613","/_next/static/chunks/3lf9kdvvybemj.js?dpl=nogit-1790362613","/_next/static/chunks/2hyw6fyf3iqeh.js?dpl=nogit-1790362613","/_next/static/chunks/03q735zs9dbpu.js?dpl=nogit-1790362613","/_next/static/chunks/3r5hh4t0jf4es.js?dpl=nogit-1790362613","/_next/static/chunks/3ml3vooxhiupb.js?dpl=nogit-1790362613","/_next/static/chunks/1h4wccj42vygd.js?dpl=nogit-1790362613","/_next/static/chunks/12xoy6h_w_le6.js?dpl=nogit-1790362613","/_next/static/chunks/2os7nxouq91eq.js?dpl=nogit-1790362613","/_next/static/chunks/3ht89vb0p09bm.js?dpl=nogit-1790362613","/_next/static/chunks/3ocoqwe4aht_u.js?dpl=nogit-1790362613","/_next/static/chunks/32qmkt01ta8b2.js?dpl=nogit-1790362613","/_next/static/chunks/3jpl-42mbad5n.js?dpl=nogit-1790362613","/_next/static/chunks/3ao1re0xmmur_.js?dpl=nogit-1790362613","/_next/static/chunks/3xa2z7fbv2riw.js?dpl=nogit-1790362613","/_next/static/chunks/14kf-an-d2n-e.js?dpl=nogit-1790362613","/_next/static/chunks/381o-754ev9ia.js?dpl=nogit-1790362613","/_next/static/chunks/2tr2cll18vqv3.js?dpl=nogit-1790362613","/_next/static/chunks/0v4byuex1x38h.js?dpl=nogit-1790362613","/_next/static/chunks/3kom3ps_bn2q6.js?dpl=nogit-1790362613","/_next/static/chunks/1x_yxljsdq0vl.js?dpl=nogit-1790362613","/_next/static/chunks/1xkpwfqqdrdio.js?dpl=nogit-1790362613","/_next/static/chunks/04zr-wqafvwoa.js?dpl=nogit-1790362613","/_next/static/chunks/2dx-vzwyw9a3g.js?dpl=nogit-1790362613","/_next/static/chunks/2mv9l1xl_aa4j.js?dpl=nogit-1790362613","/_next/static/chunks/1ku-vdy4ggo41.js?dpl=nogit-1790362613","/_next/static/chunks/0k-y_4mcfub-p.js?dpl=nogit-1790362613","/_next/static/chunks/440m38krgocdi.js?dpl=nogit-1790362613","/_next/static/chunks/2p6gbbs6zvfpy.js?dpl=nogit-1790362613","/_next/static/chunks/172wsar4r7zzx.js?dpl=nogit-1790362613","/_next/static/chunks/0llqhg6-bxn_b.js?dpl=nogit-1790362613","/_next/static/chunks/1rbw_-uux6mpq.js?dpl=nogit-1790362613","/_next/static/chunks/1s6j_7_p0ugo9.js?dpl=nogit-1790362613","/_next/static/chunks/34ux0fo6f-rm8.js?dpl=nogit-1790362613","/_next/static/chunks/1pp_uf_jx5j9r.js?dpl=nogit-1790362613","/_next/static/chunks/2b6r02yb2zswo.js?dpl=nogit-1790362613","/_next/static/chunks/422ba61wql3d7.js?dpl=nogit-1790362613","/_next/static/chunks/2vg15qyptj-oc.js?dpl=nogit-1790362613","/_next/static/chunks/0d2u5k628p_lw.js?dpl=nogit-1790362613","/_next/static/chunks/3jzaxe43n3e1e.js?dpl=nogit-1790362613","/_next/static/chunks/1lsxkfxy262n-.js?dpl=nogit-1790362613","/_next/static/chunks/02e_f03j5ij1l.js?dpl=nogit-1790362613","/_next/static/chunks/12mv6p8rwcl5o.js?dpl=nogit-1790362613","/_next/static/chunks/0v5zhouho0zlq.js?dpl=nogit-1790362613","/_next/static/chunks/41x40gd5jiq0g.js?dpl=nogit-1790362613","/_next/static/chunks/2nnmvgmq4euk9.js?dpl=nogit-1790362613","/_next/static/chunks/1ksyn9m68446d.js?dpl=nogit-1790362613","/_next/static/chunks/3wqp-h5xnebw9.js?dpl=nogit-1790362613","/_next/static/chunks/30dopbgd1dkf9.js?dpl=nogit-1790362613","/_next/static/chunks/22z8pa0ys3w4l.js?dpl=nogit-1790362613","/_next/static/chunks/0zg1om_k0m5zv.js?dpl=nogit-1790362613","/_next/static/chunks/2ywf8cxod8dkv.js?dpl=nogit-1790362613","/_next/static/chunks/43ajf4ofaeu5y.js?dpl=nogit-1790362613","/_next/static/chunks/1__39-dgg7p8-.js?dpl=nogit-1790362613","/_next/static/chunks/1zt4k83kx3bkw.js?dpl=nogit-1790362613","/_next/static/chunks/0rt2_go1it43r.js?dpl=nogit-1790362613","/_next/static/chunks/200x0be4hbjpj.js?dpl=nogit-1790362613","/_next/static/chunks/35bn8r0ao86_s.js?dpl=nogit-1790362613","/_next/static/chunks/3xskuweujaw05.js?dpl=nogit-1790362613","/_next/static/chunks/2wlqtkfegn9hx.js?dpl=nogit-1790362613","/_next/static/chunks/2y341-r8ncizo.js?dpl=nogit-1790362613","/_next/static/chunks/03ai9i_h50rnc.js?dpl=nogit-1790362613","/_next/static/chunks/0pdzmybpnr872.js?dpl=nogit-1790362613"],"TopicQuestionBank"] 25:["$","$L37",null,{"bundle":{"topicIds":["bb070e83-5617-4b2d-a167-e007ba2a6d42"],"paperIds":[],"stageIds":[],"stageTopicIds":[],"stageAssessmentIds":[],"topicNoteIds":[]},"children":[["$","$L38",null,{"feature":"question-bank"}],"$L39",["$","$L3a",null,{"subjectCode":"a_level_maths__aqa","subjectName":"Maths","topicSlug":"product-quotient-and-chain-rules","topicTitle":"1.10.4 Product, quotient and chain rules (A-level only)","sectionTitle":null,"activity":"worksheet","resourceTitle":"1.10.4 Product, quotient and chain rules (A-level only) Questions","resourceHref":"/a-level/maths/aqa/product-quotient-and-chain-rules/questions/q1","saveTrail":false}],["$","$L3b",null,{"href":"/a-level/maths/aqa/product-quotient-and-chain-rules/questions/q1","label":"1.10.4 Product, quotient and chain rules (A-level only)","subjectCode":"a_level_maths__aqa","surface":"questions"}],["$","script",null,{"type":"application/ld+json","dangerouslySetInnerHTML":{"__html":"{\"@context\":\"https://schema.org\",\"@type\":\"LearningResource\",\"name\":\"Question 11 – 1.10.4 Product, quotient and chain rules (A-level only) - Questions\",\"description\":\"Practise 1.10.4 Product, quotient and chain rules (A-level only) A Level Maths exam-style questions with worked solutions on MathsGenie.\",\"learningResourceType\":\"Practice questions\",\"educationalLevel\":\"A Level\",\"about\":{\"@type\":\"Thing\",\"name\":\"1.10.4 Product, quotient and chain rules (A-level only)\"},\"url\":\"https://mathsgenie.co.uk/a-level/maths/aqa/product-quotient-and-chain-rules/questions/q11\",\"inLanguage\":\"en-GB\",\"provider\":{\"@id\":\"https://mathsgenie.co.uk/#organization\"}}"}}],["$","div",null,{"className":"min-h-0 w-full flex-1 overflow-hidden bg-background","children":["$","$L3c",null,{"backHref":"/a-level/maths/aqa/questions","basePath":"/a-level/maths/aqa/product-quotient-and-chain-rules/questions","formulaUrl":"https://filestore.aqa.org.uk/resources/mathematics/AQA-AS-A-MATHS-FORMULAE.PDF","initialIndex":10,"initialQuestionWindow":[{"id":"d6515a96-3299-4394-97bc-a7029aa939de","revisionId":"141d3396-0c34-4a71-874a-cf664cda925c","questionNumber":null,"questionType":"LA","specification":"Differentiate with respect to $x$,","difficulty":1,"difficultyBand":"easy","tier":null,"totalMarks":4,"sourceTitle":null,"calculatorUse":null,"isCalculation":true,"parts":[{"id":"20b6f7eb-bc93-4ce4-bae5-6f4c6a0c5d41","label":"a","content":"$$3x^4 + e^{5x}$","markscheme":"- Differentiates $3x^4$ to $12x^3$ B1\n- Differentiates $e^{5x}$ to $5e^{5x}$ B1","marks":2,"order":0,"markingRubric":{"totalMarks":2,"points":[{"id":"p1","marks":1,"description":"Differentiates the polynomial term correctly to $12x^3$","code":"B"},{"id":"p2","marks":1,"description":"Differentiates the exponential term correctly to $5e^{5x}$","code":"B"}],"finalAnswers":["12x^3 + 5e^{5x}"],"generatedAt":"2026-05-06T14:03:48.787Z","modelVersion":"gemini-3-flash-preview"},"tableImages":[],"explanation":{"methods":[{"id":"direct_differentiation","label":"Direct Differentiation","steps":[{"type":"text","order":0,"title":"Identify the terms","content":"We need to find the derivative of the expression with respect to $x$:\n\n$$y = 3x^4 + e^{5x}$$\n\nUsing the sum rule for differentiation, we can differentiate each term independently:\n\n$$\\frac{dy}{dx} = \\frac{d}{dx}\\left(3x^4\\right) + \\frac{d}{dx}\\left(e^{5x}\\right)$$"},{"type":"hyper_latex","block":{"nodes":[{"latex":"$$\\text{Power Rule: } \\frac{d}{dx}(x^n) = n x^{n-1}$"},{"latex":"$$\\frac{d}{dx}\\left(\\htmlData{anchor=alg-term}{\\color{@sky}{3x^4}}\\right) = 3 \\cdot \\htmlData{anchor=power-step}{\\color{@sky}{4x^{4-1}}}$"},{"latex":"$$\\phantom{\\frac{d}{dx}\\left(3x^4\\right)} = \\htmlData{anchor=alg-deriv}{\\color{@sky}{12x^3}}$"}],"highlights":[{"color":"sky","style":"text-color","anchor":"alg-term"},{"color":"sky","style":"text-color","anchor":"alg-deriv"}],"connections":[{"to":"power-step","from":"alg-term","color":"sky","label":"multiply exponent","style":"solid"},{"to":"alg-deriv","from":"power-step","color":"sky","label":"simplify","style":"solid"}]},"order":1,"title":"Differentiate algebraic term","description":"First, we apply the power rule to the algebraic term $3x^4$. Multiply the coefficient by the exponent and subtract $1$ from the power. This earns you the first mark."},{"type":"hyper_latex","block":{"nodes":[{"latex":"$$\\text{Chain Rule: } \\frac{d}{dx}\\left(e^{f(x)}\\right) = f'(x)e^{f(x)}$"},{"latex":"$$\\frac{d}{dx}\\left(\\htmlData{anchor=exp-term}{\\color{@purple}{e^{5x}}}\\right) = \\htmlData{anchor=inner-deriv}{\\color{@purple}{\\frac{d}{dx}(5x)}} \\cdot e^{5x}$"},{"latex":"$$\\phantom{\\frac{d}{dx}\\left(e^{5x}\\right)} = \\htmlData{anchor=exp-deriv}{\\color{@purple}{5e^{5x}}}$"}],"highlights":[{"color":"purple","style":"text-color","anchor":"exp-term"},{"color":"purple","style":"text-color","anchor":"exp-deriv"}],"connections":[{"to":"inner-deriv","from":"exp-term","color":"purple","label":"chain rule","style":"solid"},{"to":"exp-deriv","from":"inner-deriv","color":"purple","label":"simplify","style":"solid"}]},"order":2,"title":"Differentiate exponential term","description":"Next, we differentiate the exponential term $e^{5x}$ using the chain rule. The derivative of $e^{kx}$ is $k e^{kx}$. This earns you the second mark."},{"type":"text","order":3,"title":"Combine the results","content":"Now we combine both independent derivatives to get the final result:\n\n$$\\frac{dy}{dx} = 12x^3 + 5e^{5x}$$"}]}],"generatedAt":"2026-06-09T09:51:51.585Z","modelVersion":"gemini-3.5-flash","explanationVersion":"v2"},"options":[]},{"id":"7e08d275-ccb0-49aa-bc42-1d29428d627e","label":"b","content":"$$(x^2 + 7)^4$","markscheme":"- Applies chain rule: $4(x^2 + 7)^3 \\times \\dots$ M1\n- Correct derivative $8x(x^2 + 7)^3$ A1","marks":2,"order":1,"markingRubric":{"totalMarks":2,"points":[{"id":"p1","marks":1,"description":"Applies the chain rule correctly, identifying the outer function derivative as $4(x^2 + 7)^3$","code":"M"},{"id":"p2","marks":1,"description":"Multiplies by the inner derivative $2x$ and simplifies to $8x(x^2 + 7)^3$","code":"A"}],"finalAnswers":["8x(x^2 + 7)^3"],"generatedAt":"2026-05-06T14:03:48.787Z","modelVersion":"gemini-3-flash-preview"},"tableImages":[],"explanation":{"methods":[{"id":"chain_rule_direct","label":"Direct Chain Rule","steps":[{"type":"text","order":0,"title":"Identify the composite function","content":"We want to differentiate the function $y = (x^2 + 7)^4$ with respect to $x$.\n\nThis is a composite function of the form $y = [f(x)]^n$:\n- The **outer function** is the power function: $[\\dots]^4$\n- The **inner function** is the quadratic expression: $x^2 + 7$\n\nTo find the derivative, we can apply the **Direct Chain Rule**.","highlights":[{"text":"$$(x^2 + 7)^4$","location":"specification"}]},{"type":"text","order":1,"title":"Recall the Direct Chain Rule","content":"The **Direct Chain Rule** allows us to differentiate a composite function directly in one step:\n\n$$\\frac{d}{dx}\\left([f(x)]^n\\right) = n[f(x)]^{n-1} \\times f'(x)$$\n\nThis means we:\n1. Differentiate the outer function, keeping the inner function $f(x)$ exactly as it is.\n2. Multiply the result by the derivative of the inner function, $f'(x)$."},{"type":"hyper_latex","block":{"nodes":[{"latex":"$$y = (\\htmlData{anchor=inner-orig}{\\color{@sky}{x^2 + 7}})^{\\htmlData{anchor=power-orig}{\\color{@amber}{4}}}$"},{"latex":"$$\\frac{dy}{dx} = \\htmlData{anchor=power-diff}{\\color{@amber}{4}}(\\htmlData{anchor=inner-keep}{\\color{@sky}{x^2 + 7}})^{\\htmlData{anchor=power-sub}{\\color{@amber}{3}}} \\times \\frac{d}{dx}(\\htmlData{anchor=inner-deriv}{\\color{@sky}{x^2 + 7}})$"}],"highlights":[{"color":"sky","style":"underline","anchor":"inner-orig"},{"color":"amber","style":"text-color","anchor":"power-orig"},{"color":"amber","style":"text-color","anchor":"power-diff"},{"color":"amber","style":"text-color","anchor":"power-sub"}],"connections":[{"to":"power-diff","from":"power-orig","color":"amber","label":"multiply by power","style":"solid"},{"to":"inner-keep","from":"inner-orig","color":"sky","label":"keep inner function","style":"solid"}]},"order":2,"title":"Differentiate the outer function","description":"First, we apply the power rule to the outer function, bringing the power of $4$ to the front and reducing the power by $1$ to get $3$, whilst keeping the inner function $x^2 + 7$ unchanged."},{"type":"text","order":3,"title":"Differentiate the inner function","content":"Now, we differentiate the inner function $x^2 + 7$ with respect to $x$:\n\n$$\\frac{d}{dx}(x^2 + 7) = 2x$$\n\nSubstituting this back into our expression gives us:\n\n$$\\frac{dy}{dx} = 4(x^2 + 7)^3 \\times 2x$$\n\nThis step earns the method mark **M1** under the exam markscheme."},{"type":"text","order":4,"title":"Simplify to find final answer","content":"Finally, we simplify the expression by multiplying the coefficients together:\n\n$$\\frac{dy}{dx} = 4 \\times 2x \\times (x^2 + 7)^3 = 8x(x^2 + 7)^3$$\n\nThis completes our differentiation and earns the accuracy mark **A1**.\n\n$$\\text{Final Answer: } 8x(x^2 + 7)^3$$"}]},{"id":"chain_rule_substitution","label":"Chain Rule with Substitution","steps":[{"type":"text","order":0,"title":"Define the intermediate variable","content":"To differentiate the composite function $y = (x^2 + 7)^4$ using substitution, we start by defining an intermediate variable $u$ for the inner function:\n\n$$u = x^2 + 7$$\n\nThis allows us to rewrite $y$ as a simpler function of $u$:\n\n$$y = u^4$$"},{"type":"hyper_latex","block":{"nodes":[{"latex":"$$y = \\htmlData{anchor=u-func}{u^4} \\implies \\frac{dy}{du} = \\htmlData{anchor=dy-du}{\\color{@sky}{4u^3}}$"},{"text":"And for the inner function:"},{"latex":"$$u = \\htmlData{anchor=x-func}{x^2 + 7} \\implies \\frac{du}{dx} = \\htmlData{anchor=du-dx}{\\color{@amber}{2x}}$"}],"highlights":[{"color":"sky","style":"text-color","anchor":"dy-du"},{"color":"amber","style":"text-color","anchor":"du-dx"}],"connections":[{"to":"dy-du","from":"u-func","color":"sky","label":"power rule","style":"solid"},{"to":"du-dx","from":"x-func","color":"amber","label":"power rule","style":"solid"}]},"order":1,"title":"Find the individual derivatives","description":"Now, we find the derivative of each function individually using the power rule."},{"type":"hyper_latex","block":{"nodes":[{"latex":"$$\\frac{dy}{dx} = \\htmlData{anchor=chain-dy-du}{\\frac{dy}{du}} \\times \\htmlData{anchor=chain-du-dx}{\\frac{du}{dx}}$"},{"latex":"$$\\frac{dy}{dx} = (\\htmlData{anchor=sub-dy-du}{\\color{@sky}{4u^3}}) \\times (\\htmlData{anchor=sub-du-dx}{\\color{@amber}{2x}})$"}],"highlights":[{"color":"sky","style":"text-color","anchor":"sub-dy-du"},{"color":"amber","style":"text-color","anchor":"sub-du-dx"}],"connections":[{"to":"sub-dy-du","from":"chain-dy-du","color":"sky","label":null,"style":"solid"},{"to":"sub-du-dx","from":"chain-du-dx","color":"amber","label":null,"style":"solid"}]},"order":2,"title":"Apply the Chain Rule","description":"The Chain Rule states that we multiply these two derivatives together."},{"type":"text","order":3,"title":"Substitute back and simplify","content":"Finally, we substitute the expression for $u$ back into our derivative to get the final answer in terms of $x$:\n\n$$\\begin{aligned} \\frac{dy}{dx} &= 4(x^2 + 7)^3 \\times 2x \\\\ &= 8x(x^2 + 7)^3 \\end{aligned}$$\n\nApplying the chain rule correctly earns you the first mark M1, and simplifying to the final correct derivative earns the second mark A1."}]},{"id":"binomial_expansion","label":"Binomial Expansion","steps":[{"type":"text","order":0,"title":"Identify the approach","content":"We need to find the derivative of $(x^2 + 7)^4$ with respect to $x$. While this is typically solved using the chain rule, we will use the **Binomial Expansion** method. We will first expand the expression fully and then differentiate it term by term."},{"type":"text","order":1,"title":"Recall the binomial theorem","content":"The general formula for expanding a binomial of the form $(a + b)^n$ is:\n\n$$(a + b)^n = \\sum_{r=0}^{n} \\binom{n}{r} a^{n-r} b^r$$\n\nIn our case, we have:\n- $a = x^2$\n- $b = 7$\n- $n = 4$"},{"type":"text","order":2,"title":"Expand the expression","content":"Let's expand $(x^2 + 7)^4$ term by term using the binomial coefficients for $n=4$, which are $1, 4, 6, 4, 1$:\n\n$$\\begin{aligned} (x^2 + 7)^4 &= \\binom{4}{0}(x^2)^4(7)^0 + \\binom{4}{1}(x^2)^3(7)^1 + \\binom{4}{2}(x^2)^2(7)^2 + \\binom{4}{3}(x^2)^1(7)^3 + \\binom{4}{4}(x^2)^0(7)^4 \\\\ &= 1(x^8)(1) + 4(x^6)(7) + 6(x^4)(49) + 4(x^2)(343) + 1(1)(2401) \\\\ &= x^8 + 28x^6 + 294x^4 + 1372x^2 + 2401 \\end{aligned}$$"},{"type":"text","order":3,"title":"Differentiate term by term","content":"Now we differentiate each term of the expanded polynomial with respect to $x$ using the power rule, $\\frac{d}{dx}(x^n) = nx^{n-1}$:\n\n$$\\begin{aligned} \\frac{d}{dx}\\left( (x^2 + 7)^4 \\right) &= \\frac{d}{dx}(x^8 + 28x^6 + 294x^4 + 1372x^2 + 2401) \\\\ &= 8x^7 + 28(6x^5) + 294(4x^3) + 1372(2x) + 0 \\\\ &= 8x^7 + 168x^5 + 1176x^3 + 2744x \\end{aligned}$$"},{"type":"text","order":4,"title":"Factorise the derivative","content":"To simplify our answer and match it to the standard chain rule format, we can factorise out the common term $8x$:\n\n$$8x^7 + 168x^5 + 1176x^3 + 2744x = 8x(x^6 + 21x^4 + 147x^2 + 343)$$\n\nNotice that the terms inside the parentheses can be rewritten as $(x^2 + 7)^3$ since:\n\n$$(x^2 + 7)^3 = (x^2)^3 + 3(x^2)^2(7) + 3(x^2)(7^2) + 7^3 = x^6 + 21x^4 + 147x^2 + 343$$\n\nThus, the simplified derivative is:\n\n$$8x(x^2 + 7)^3$$"}]}],"generatedAt":"2026-06-09T09:52:24.890Z","modelVersion":"gemini-3.5-flash","explanationVersion":"v2"},"options":[]}],"options":[],"explanation":{"methods":[{"id":"20b6f7eb-bc93-4ce4-bae5-6f4c6a0c5d41:direct_differentiation","label":"(a) Direct Differentiation","steps":[{"type":"text","order":0,"title":"Identify the terms","content":"We need to find the derivative of the expression with respect to $x$:\n\n$$y = 3x^4 + e^{5x}$$\n\nUsing the sum rule for differentiation, we can differentiate each term independently:\n\n$$\\frac{dy}{dx} = \\frac{d}{dx}\\left(3x^4\\right) + \\frac{d}{dx}\\left(e^{5x}\\right)$$"},{"type":"hyper_latex","block":{"nodes":[{"latex":"$$\\text{Power Rule: } \\frac{d}{dx}(x^n) = n x^{n-1}$"},{"latex":"$$\\frac{d}{dx}\\left(\\htmlData{anchor=alg-term}{\\color{@sky}{3x^4}}\\right) = 3 \\cdot \\htmlData{anchor=power-step}{\\color{@sky}{4x^{4-1}}}$"},{"latex":"$$\\phantom{\\frac{d}{dx}\\left(3x^4\\right)} = \\htmlData{anchor=alg-deriv}{\\color{@sky}{12x^3}}$"}],"highlights":[{"color":"sky","style":"text-color","anchor":"alg-term"},{"color":"sky","style":"text-color","anchor":"alg-deriv"}],"connections":[{"to":"power-step","from":"alg-term","color":"sky","label":"multiply exponent","style":"solid"},{"to":"alg-deriv","from":"power-step","color":"sky","label":"simplify","style":"solid"}]},"order":1,"title":"Differentiate algebraic term","description":"First, we apply the power rule to the algebraic term $3x^4$. Multiply the coefficient by the exponent and subtract $1$ from the power. This earns you the first mark."},{"type":"hyper_latex","block":{"nodes":[{"latex":"$$\\text{Chain Rule: } \\frac{d}{dx}\\left(e^{f(x)}\\right) = f'(x)e^{f(x)}$"},{"latex":"$$\\frac{d}{dx}\\left(\\htmlData{anchor=exp-term}{\\color{@purple}{e^{5x}}}\\right) = \\htmlData{anchor=inner-deriv}{\\color{@purple}{\\frac{d}{dx}(5x)}} \\cdot e^{5x}$"},{"latex":"$$\\phantom{\\frac{d}{dx}\\left(e^{5x}\\right)} = \\htmlData{anchor=exp-deriv}{\\color{@purple}{5e^{5x}}}$"}],"highlights":[{"color":"purple","style":"text-color","anchor":"exp-term"},{"color":"purple","style":"text-color","anchor":"exp-deriv"}],"connections":[{"to":"inner-deriv","from":"exp-term","color":"purple","label":"chain rule","style":"solid"},{"to":"exp-deriv","from":"inner-deriv","color":"purple","label":"simplify","style":"solid"}]},"order":2,"title":"Differentiate exponential term","description":"Next, we differentiate the exponential term $e^{5x}$ using the chain rule. The derivative of $e^{kx}$ is $k e^{kx}$. This earns you the second mark."},{"type":"text","order":3,"title":"Combine the results","content":"Now we combine both independent derivatives to get the final result:\n\n$$\\frac{dy}{dx} = 12x^3 + 5e^{5x}$$"}]},{"id":"7e08d275-ccb0-49aa-bc42-1d29428d627e:chain_rule_direct","label":"(b) Direct Chain Rule","steps":[{"type":"text","order":0,"title":"Identify the composite function","content":"We want to differentiate the function $y = (x^2 + 7)^4$ with respect to $x$.\n\nThis is a composite function of the form $y = [f(x)]^n$:\n- The **outer function** is the power function: $[\\dots]^4$\n- The **inner function** is the quadratic expression: $x^2 + 7$\n\nTo find the derivative, we can apply the **Direct Chain Rule**.","highlights":[{"text":"$$(x^2 + 7)^4$","location":"specification"}]},{"type":"text","order":1,"title":"Recall the Direct Chain Rule","content":"The **Direct Chain Rule** allows us to differentiate a composite function directly in one step:\n\n$$\\frac{d}{dx}\\left([f(x)]^n\\right) = n[f(x)]^{n-1} \\times f'(x)$$\n\nThis means we:\n1. Differentiate the outer function, keeping the inner function $f(x)$ exactly as it is.\n2. Multiply the result by the derivative of the inner function, $f'(x)$."},{"type":"hyper_latex","block":{"nodes":[{"latex":"$$y = (\\htmlData{anchor=inner-orig}{\\color{@sky}{x^2 + 7}})^{\\htmlData{anchor=power-orig}{\\color{@amber}{4}}}$"},{"latex":"$$\\frac{dy}{dx} = \\htmlData{anchor=power-diff}{\\color{@amber}{4}}(\\htmlData{anchor=inner-keep}{\\color{@sky}{x^2 + 7}})^{\\htmlData{anchor=power-sub}{\\color{@amber}{3}}} \\times \\frac{d}{dx}(\\htmlData{anchor=inner-deriv}{\\color{@sky}{x^2 + 7}})$"}],"highlights":[{"color":"sky","style":"underline","anchor":"inner-orig"},{"color":"amber","style":"text-color","anchor":"power-orig"},{"color":"amber","style":"text-color","anchor":"power-diff"},{"color":"amber","style":"text-color","anchor":"power-sub"}],"connections":[{"to":"power-diff","from":"power-orig","color":"amber","label":"multiply by power","style":"solid"},{"to":"inner-keep","from":"inner-orig","color":"sky","label":"keep inner function","style":"solid"}]},"order":2,"title":"Differentiate the outer function","description":"First, we apply the power rule to the outer function, bringing the power of $4$ to the front and reducing the power by $1$ to get $3$, whilst keeping the inner function $x^2 + 7$ unchanged."},{"type":"text","order":3,"title":"Differentiate the inner function","content":"Now, we differentiate the inner function $x^2 + 7$ with respect to $x$:\n\n$$\\frac{d}{dx}(x^2 + 7) = 2x$$\n\nSubstituting this back into our expression gives us:\n\n$$\\frac{dy}{dx} = 4(x^2 + 7)^3 \\times 2x$$\n\nThis step earns the method mark **M1** under the exam markscheme."},{"type":"text","order":4,"title":"Simplify to find final answer","content":"Finally, we simplify the expression by multiplying the coefficients together:\n\n$$\\frac{dy}{dx} = 4 \\times 2x \\times (x^2 + 7)^3 = 8x(x^2 + 7)^3$$\n\nThis completes our differentiation and earns the accuracy mark **A1**.\n\n$$\\text{Final Answer: } 8x(x^2 + 7)^3$$"}]},{"id":"7e08d275-ccb0-49aa-bc42-1d29428d627e:chain_rule_substitution","label":"(b) Chain Rule with Substitution","steps":[{"type":"text","order":0,"title":"Define the intermediate variable","content":"To differentiate the composite function $y = (x^2 + 7)^4$ using substitution, we start by defining an intermediate variable $u$ for the inner function:\n\n$$u = x^2 + 7$$\n\nThis allows us to rewrite $y$ as a simpler function of $u$:\n\n$$y = u^4$$"},{"type":"hyper_latex","block":{"nodes":[{"latex":"$$y = \\htmlData{anchor=u-func}{u^4} \\implies \\frac{dy}{du} = \\htmlData{anchor=dy-du}{\\color{@sky}{4u^3}}$"},{"text":"And for the inner function:"},{"latex":"$$u = \\htmlData{anchor=x-func}{x^2 + 7} \\implies \\frac{du}{dx} = \\htmlData{anchor=du-dx}{\\color{@amber}{2x}}$"}],"highlights":[{"color":"sky","style":"text-color","anchor":"dy-du"},{"color":"amber","style":"text-color","anchor":"du-dx"}],"connections":[{"to":"dy-du","from":"u-func","color":"sky","label":"power rule","style":"solid"},{"to":"du-dx","from":"x-func","color":"amber","label":"power rule","style":"solid"}]},"order":1,"title":"Find the individual derivatives","description":"Now, we find the derivative of each function individually using the power rule."},{"type":"hyper_latex","block":{"nodes":[{"latex":"$$\\frac{dy}{dx} = \\htmlData{anchor=chain-dy-du}{\\frac{dy}{du}} \\times \\htmlData{anchor=chain-du-dx}{\\frac{du}{dx}}$"},{"latex":"$$\\frac{dy}{dx} = (\\htmlData{anchor=sub-dy-du}{\\color{@sky}{4u^3}}) \\times (\\htmlData{anchor=sub-du-dx}{\\color{@amber}{2x}})$"}],"highlights":[{"color":"sky","style":"text-color","anchor":"sub-dy-du"},{"color":"amber","style":"text-color","anchor":"sub-du-dx"}],"connections":[{"to":"sub-dy-du","from":"chain-dy-du","color":"sky","label":null,"style":"solid"},{"to":"sub-du-dx","from":"chain-du-dx","color":"amber","label":null,"style":"solid"}]},"order":2,"title":"Apply the Chain Rule","description":"The Chain Rule states that we multiply these two derivatives together."},{"type":"text","order":3,"title":"Substitute back and simplify","content":"Finally, we substitute the expression for $u$ back into our derivative to get the final answer in terms of $x$:\n\n$$\\begin{aligned} \\frac{dy}{dx} &= 4(x^2 + 7)^3 \\times 2x \\\\ &= 8x(x^2 + 7)^3 \\end{aligned}$$\n\nApplying the chain rule correctly earns you the first mark M1, and simplifying to the final correct derivative earns the second mark A1."}]},{"id":"7e08d275-ccb0-49aa-bc42-1d29428d627e:binomial_expansion","label":"(b) Binomial Expansion","steps":[{"type":"text","order":0,"title":"Identify the approach","content":"We need to find the derivative of $(x^2 + 7)^4$ with respect to $x$. While this is typically solved using the chain rule, we will use the **Binomial Expansion** method. We will first expand the expression fully and then differentiate it term by term."},{"type":"text","order":1,"title":"Recall the binomial theorem","content":"The general formula for expanding a binomial of the form $(a + b)^n$ is:\n\n$$(a + b)^n = \\sum_{r=0}^{n} \\binom{n}{r} a^{n-r} b^r$$\n\nIn our case, we have:\n- $a = x^2$\n- $b = 7$\n- $n = 4$"},{"type":"text","order":2,"title":"Expand the expression","content":"Let's expand $(x^2 + 7)^4$ term by term using the binomial coefficients for $n=4$, which are $1, 4, 6, 4, 1$:\n\n$$\\begin{aligned} (x^2 + 7)^4 &= \\binom{4}{0}(x^2)^4(7)^0 + \\binom{4}{1}(x^2)^3(7)^1 + \\binom{4}{2}(x^2)^2(7)^2 + \\binom{4}{3}(x^2)^1(7)^3 + \\binom{4}{4}(x^2)^0(7)^4 \\\\ &= 1(x^8)(1) + 4(x^6)(7) + 6(x^4)(49) + 4(x^2)(343) + 1(1)(2401) \\\\ &= x^8 + 28x^6 + 294x^4 + 1372x^2 + 2401 \\end{aligned}$$"},{"type":"text","order":3,"title":"Differentiate term by term","content":"Now we differentiate each term of the expanded polynomial with respect to $x$ using the power rule, $\\frac{d}{dx}(x^n) = nx^{n-1}$:\n\n$$\\begin{aligned} \\frac{d}{dx}\\left( (x^2 + 7)^4 \\right) &= \\frac{d}{dx}(x^8 + 28x^6 + 294x^4 + 1372x^2 + 2401) \\\\ &= 8x^7 + 28(6x^5) + 294(4x^3) + 1372(2x) + 0 \\\\ &= 8x^7 + 168x^5 + 1176x^3 + 2744x \\end{aligned}$$"},{"type":"text","order":4,"title":"Factorise the derivative","content":"To simplify our answer and match it to the standard chain rule format, we can factorise out the common term $8x$:\n\n$$8x^7 + 168x^5 + 1176x^3 + 2744x = 8x(x^6 + 21x^4 + 147x^2 + 343)$$\n\nNotice that the terms inside the parentheses can be rewritten as $(x^2 + 7)^3$ since:\n\n$$(x^2 + 7)^3 = (x^2)^3 + 3(x^2)^2(7) + 3(x^2)(7^2) + 7^3 = x^6 + 21x^4 + 147x^2 + 343$$\n\nThus, the simplified derivative is:\n\n$$8x(x^2 + 7)^3$$"}]}],"generatedAt":"2026-06-09T09:52:36.696Z","modelVersion":"gemini-3.5-flash","explanationVersion":"v2"},"firstAttemptFullMarks":{"percent":88},"walkthroughVideo":null}],"subjectCode":"a_level_maths__aqa","summaries":[{"id":"43670804-b308-4c43-b1b0-15ba09240572","difficultyBand":"medium","calculatorUse":null,"totalMarks":8,"questionType":"LA","isCalculation":true},{"id":"6dd38f5a-9457-41f6-bdd8-5f51fb66d919","difficultyBand":"medium","calculatorUse":null,"totalMarks":8,"questionType":"LA","isCalculation":true},{"id":"e0b9b73d-7217-4a30-9f07-a62b43ccabce","difficultyBand":"medium","calculatorUse":null,"totalMarks":5,"questionType":"LA","isCalculation":true},{"id":"218d405b-a791-47c6-a02e-ddde693db591","difficultyBand":"medium","calculatorUse":null,"totalMarks":4,"questionType":"LA","isCalculation":true},{"id":"233cef29-b34e-452d-b329-eeb2f8d1af50","difficultyBand":"medium","calculatorUse":null,"totalMarks":8,"questionType":"LA","isCalculation":true},{"id":"423b5f9a-ebf5-4f40-82a1-09c4061ade2b","difficultyBand":"medium","calculatorUse":null,"totalMarks":5,"questionType":"LA","isCalculation":false},{"id":"5e22ee31-8d84-465e-9ae7-5f3393f1bbcc","difficultyBand":"medium","calculatorUse":null,"totalMarks":7,"questionType":"LA","isCalculation":true},{"id":"6b16a43e-76ff-4df7-942f-0b53c44f143b","difficultyBand":"medium","calculatorUse":null,"totalMarks":5,"questionType":"LA","isCalculation":false},{"id":"8423de37-6e55-4383-8387-71cd38a57705","difficultyBand":"medium","calculatorUse":null,"totalMarks":5,"questionType":"LA","isCalculation":true},{"id":"aabe4c72-d7d0-43ee-9c1d-1a1b6470204a","difficultyBand":"medium","calculatorUse":null,"totalMarks":6,"questionType":"LA","isCalculation":false},{"id":"d6515a96-3299-4394-97bc-a7029aa939de","difficultyBand":"easy","calculatorUse":null,"totalMarks":4,"questionType":"LA","isCalculation":true},{"id":"d7542af0-c3ba-44ed-81cd-ab6ab6f8a30a","difficultyBand":"medium","calculatorUse":null,"totalMarks":7,"questionType":"LA","isCalculation":true},{"id":"dcc84617-b6eb-4564-b8e5-ed5142a90f67","difficultyBand":"medium","calculatorUse":null,"totalMarks":7,"questionType":"LA","isCalculation":true},{"id":"e10def56-640b-416a-b974-27935fa57ad3","difficultyBand":"medium","calculatorUse":null,"totalMarks":6,"questionType":"LA","isCalculation":true},{"id":"ed0d3408-c4dc-41f2-9018-0ac8079562aa","difficultyBand":"medium","calculatorUse":null,"totalMarks":5,"questionType":"LA","isCalculation":true},{"id":"ee8cc8d3-1b89-4d8b-8908-fe61c14cee60","difficultyBand":"medium","calculatorUse":null,"totalMarks":6,"questionType":"LA","isCalculation":true},{"id":"ef7406ef-b962-485d-967b-263dbf039539","difficultyBand":"medium","calculatorUse":null,"totalMarks":8,"questionType":"LA","isCalculation":true},{"id":"f2d4c50a-dfb8-4a87-a753-18a9f23a84cc","difficultyBand":"medium","calculatorUse":null,"totalMarks":6,"questionType":"LA","isCalculation":true},{"id":"fcc4935a-6dc7-4c9c-afb0-ba70d84f23a6","difficultyBand":"medium","calculatorUse":null,"totalMarks":5,"questionType":"LA","isCalculation":false},{"id":"66f47b42-061b-447f-af98-b82c19ee318b","difficultyBand":"medium","calculatorUse":null,"totalMarks":6,"questionType":"LA","isCalculation":true},{"id":"783d7795-137b-4822-be83-d9c1d55fe34c","difficultyBand":"medium","calculatorUse":null,"totalMarks":5,"questionType":"LA","isCalculation":false},{"id":"a1ddd745-946c-48b3-92c5-c597b48104e1","difficultyBand":"medium","calculatorUse":null,"totalMarks":4,"questionType":"LA","isCalculation":true},{"id":"c3f9a0ad-9898-4b93-8e8f-6da9a3e5e6b5","difficultyBand":"medium","calculatorUse":null,"totalMarks":5,"questionType":"LA","isCalculation":true},{"id":"0720e9a2-40c4-4527-8636-f1396bc14a09","difficultyBand":"medium","calculatorUse":null,"totalMarks":8,"questionType":"LA","isCalculation":true},{"id":"1fe24200-387c-4d5a-aadd-796df3778a45","difficultyBand":"medium","calculatorUse":null,"totalMarks":7,"questionType":"LA","isCalculation":true},{"id":"324c01fc-3c23-4838-a251-2b61cef38926","difficultyBand":"medium","calculatorUse":null,"totalMarks":6,"questionType":"LA","isCalculation":false},{"id":"3982979a-c184-4cab-bb0c-9106d55688fd","difficultyBand":"medium","calculatorUse":null,"totalMarks":8,"questionType":"LA","isCalculation":true},{"id":"4af8e31a-8a63-44a3-8769-01cd5abb9467","difficultyBand":"medium","calculatorUse":null,"totalMarks":7,"questionType":"LA","isCalculation":true},{"id":"6c577d2b-91b1-48d8-b0d0-44c32c8af6a3","difficultyBand":"medium","calculatorUse":null,"totalMarks":6,"questionType":"LA","isCalculation":true},{"id":"8aa09984-dd36-4279-bf61-a0159bfd11d4","difficultyBand":"medium","calculatorUse":null,"totalMarks":6,"questionType":"LA","isCalculation":false},{"id":"9548d2cd-09f8-45c9-8239-a49aa6d6bb6d","difficultyBand":"medium","calculatorUse":null,"totalMarks":7,"questionType":"LA","isCalculation":true},{"id":"9ec7b6f4-b03d-4589-a8f9-3cce13a23630","difficultyBand":"medium","calculatorUse":null,"totalMarks":6,"questionType":"LA","isCalculation":true},{"id":"a23f2c36-7e47-4e8e-a2ae-55dd51cc1c54","difficultyBand":"medium","calculatorUse":null,"totalMarks":5,"questionType":"LA","isCalculation":false},{"id":"b688a254-1710-4fae-ba71-47995d3640d7","difficultyBand":"medium","calculatorUse":null,"totalMarks":5,"questionType":"LA","isCalculation":true},{"id":"dbc20d6a-c369-4c4b-bb83-24d4f2a2960a","difficultyBand":"easy","calculatorUse":null,"totalMarks":4,"questionType":"LA","isCalculation":true},{"id":"ddf74e3d-06cc-4ae0-ae14-1c0265aa5c88","difficultyBand":"medium","calculatorUse":null,"totalMarks":6,"questionType":"LA","isCalculation":true},{"id":"e4445615-392a-4489-a971-796a61ff8a33","difficultyBand":"medium","calculatorUse":null,"totalMarks":9,"questionType":"LA","isCalculation":true},{"id":"e47704c0-2112-49f9-a2ff-659a3318916c","difficultyBand":"medium","calculatorUse":null,"totalMarks":5,"questionType":"LA","isCalculation":false},{"id":"e90e6e7d-87c9-419a-b761-350ef207d2f5","difficultyBand":"medium","calculatorUse":null,"totalMarks":4,"questionType":"LA","isCalculation":true},{"id":"f19c6214-3584-4bc8-8bf3-48d78b7096e3","difficultyBand":"medium","calculatorUse":null,"totalMarks":5,"questionType":"LA","isCalculation":true},{"id":"1dac23ab-3f17-4825-b445-772fc700dfad","difficultyBand":"easy","calculatorUse":null,"totalMarks":4,"questionType":"LA","isCalculation":true},{"id":"68dcddf7-2ec6-4759-ae74-f44fdd72209a","difficultyBand":"medium","calculatorUse":null,"totalMarks":6,"questionType":"LA","isCalculation":true},{"id":"793ed554-c6d3-4938-832b-bf44b0830667","difficultyBand":"medium","calculatorUse":null,"totalMarks":6,"questionType":"LA","isCalculation":true},{"id":"e61c0ff6-1631-455e-aa64-bf437fe7507f","difficultyBand":"medium","calculatorUse":null,"totalMarks":6,"questionType":"LA","isCalculation":false},{"id":"002faeea-0afa-4ba5-a773-8c786542dd31","difficultyBand":"easy","calculatorUse":null,"totalMarks":4,"questionType":"LA","isCalculation":true},{"id":"550b330b-570a-46e5-aaf7-350d5365afea","difficultyBand":"medium","calculatorUse":null,"totalMarks":8,"questionType":"LA","isCalculation":true},{"id":"5ea19cbc-a34a-43e6-ae77-70f238fbae5e","difficultyBand":"medium","calculatorUse":null,"totalMarks":5,"questionType":"LA","isCalculation":false},{"id":"60601d3d-8f39-40ad-a875-04eae3ad5f41","difficultyBand":"medium","calculatorUse":null,"totalMarks":6,"questionType":"LA","isCalculation":true},{"id":"62776d45-a6ee-448a-bde0-84f38af196c4","difficultyBand":"medium","calculatorUse":null,"totalMarks":7,"questionType":"LA","isCalculation":true},{"id":"78948c35-3ae0-4e85-af96-a4ab24b2a905","difficultyBand":"medium","calculatorUse":null,"totalMarks":8,"questionType":"LA","isCalculation":true},{"id":"79329219-0030-4556-9154-62cbbc920628","difficultyBand":"medium","calculatorUse":null,"totalMarks":5,"questionType":"LA","isCalculation":true},{"id":"97b4d0a4-4cc4-4328-aafc-9e1a3535fdc8","difficultyBand":"medium","calculatorUse":null,"totalMarks":5,"questionType":"LA","isCalculation":false},{"id":"a0199f00-0e9b-4632-b5e8-c8e9a4b60474","difficultyBand":"medium","calculatorUse":null,"totalMarks":5,"questionType":"LA","isCalculation":false},{"id":"aece7605-9257-44ce-9d55-4f97e298e9e9","difficultyBand":"medium","calculatorUse":null,"totalMarks":5,"questionType":"LA","isCalculation":true},{"id":"b9cb05cf-d731-4962-afed-d69e3dacbe8f","difficultyBand":"medium","calculatorUse":null,"totalMarks":6,"questionType":"LA","isCalculation":true},{"id":"cfa845e5-c60b-4318-b581-939f3bed5fae","difficultyBand":"easy","calculatorUse":null,"totalMarks":4,"questionType":"LA","isCalculation":true},{"id":"f025819b-52f0-462a-849a-283d40022e5b","difficultyBand":"medium","calculatorUse":null,"totalMarks":6,"questionType":"LA","isCalculation":false},{"id":"f3747d18-6e6f-4b65-bd95-404d2da578e7","difficultyBand":"medium","calculatorUse":null,"totalMarks":7,"questionType":"LA","isCalculation":true},{"id":"fc58532d-2057-4310-9ca0-ac9832b1dbe5","difficultyBand":"medium","calculatorUse":null,"totalMarks":7,"questionType":"LA","isCalculation":true},{"id":"7927f933-2f36-4da9-a21e-59b05e0e6fae","difficultyBand":"medium","calculatorUse":null,"totalMarks":7,"questionType":"LA","isCalculation":true},{"id":"a0bc4f61-22ad-4bf0-9c7e-1bdd393f7849","difficultyBand":"medium","calculatorUse":null,"totalMarks":5,"questionType":"LA","isCalculation":false},{"id":"1b1db3e5-c4d6-446a-ba82-54b917bb77f8","difficultyBand":"medium","calculatorUse":null,"totalMarks":7,"questionType":"LA","isCalculation":true},{"id":"4da587a1-b7f1-4470-b353-dcd7c83dc4b3","difficultyBand":"medium","calculatorUse":null,"totalMarks":5,"questionType":"LA","isCalculation":false},{"id":"619f22d8-6582-4a8e-a8c8-fca3c4302e31","difficultyBand":"medium","calculatorUse":null,"totalMarks":7,"questionType":"LA","isCalculation":true},{"id":"7d23c57c-b4f5-49a9-a894-e3f29fa2030d","difficultyBand":null,"calculatorUse":null,"totalMarks":9,"questionType":"LA","isCalculation":true},{"id":"7e3fb7b8-070b-4716-b7f7-fc29b79956ff","difficultyBand":"medium","calculatorUse":null,"totalMarks":6,"questionType":"LA","isCalculation":false},{"id":"019ccf6b-b2d3-4898-8bd6-1b7e5b4b33ca","difficultyBand":"medium","calculatorUse":null,"totalMarks":4,"questionType":"LA","isCalculation":true},{"id":"02a4484d-6465-47f9-8569-d80bc542a95c","difficultyBand":"hard","calculatorUse":null,"totalMarks":8,"questionType":"LA","isCalculation":true},{"id":"04d7eb5e-4403-48b9-b1a2-08ee7e153fca","difficultyBand":"medium","calculatorUse":null,"totalMarks":6,"questionType":"LA","isCalculation":true},{"id":"0de699ee-92d8-42c4-a6ff-32b84bb6e495","difficultyBand":"medium","calculatorUse":null,"totalMarks":4,"questionType":"LA","isCalculation":true},{"id":"0f10c9b7-4000-4a5f-a375-8b859f75b900","difficultyBand":"medium","calculatorUse":null,"totalMarks":3,"questionType":"LA","isCalculation":true},{"id":"137c633d-888b-442a-b962-213f13a99168","difficultyBand":"medium","calculatorUse":null,"totalMarks":4,"questionType":"LA","isCalculation":true},{"id":"1dd6e7ed-234f-4728-8cdb-9ab46caf8736","difficultyBand":"medium","calculatorUse":null,"totalMarks":3,"questionType":"LA","isCalculation":false},{"id":"20427259-b3e0-420f-987f-1e1b45d1e3b4","difficultyBand":"medium","calculatorUse":null,"totalMarks":9,"questionType":"LA","isCalculation":true},{"id":"2f6116f0-43b3-4f56-973b-d6e97b734efe","difficultyBand":"medium","calculatorUse":null,"totalMarks":11,"questionType":"LA","isCalculation":true},{"id":"35a3f8d9-497f-4e3f-a86c-e098d35ca287","difficultyBand":"medium","calculatorUse":null,"totalMarks":11,"questionType":"LA","isCalculation":true},{"id":"362274ef-ce53-4c09-a816-30ac6ec89d5d","difficultyBand":"medium","calculatorUse":null,"totalMarks":7,"questionType":"LA","isCalculation":true},{"id":"39e689e7-2e31-4a3a-9d70-526672dcf8d9","difficultyBand":"medium","calculatorUse":null,"totalMarks":5,"questionType":"LA","isCalculation":true},{"id":"3afcef57-5d5d-4b3d-a83f-6139c6a94835","difficultyBand":"medium","calculatorUse":null,"totalMarks":14,"questionType":"LA","isCalculation":true},{"id":"3bd558cf-5794-4142-a5c5-bcf0e0161aca","difficultyBand":"medium","calculatorUse":null,"totalMarks":6,"questionType":"LA","isCalculation":true},{"id":"459f1ce7-63d8-41b2-b571-c050d1bef394","difficultyBand":"medium","calculatorUse":null,"totalMarks":14,"questionType":"LA","isCalculation":true},{"id":"4d0f34a1-3b64-453a-892f-ddeb3719735f","difficultyBand":"medium","calculatorUse":null,"totalMarks":6,"questionType":"LA","isCalculation":true},{"id":"4f9e9f2d-0bd6-4a39-a10f-e80fc9c5d1b0","difficultyBand":"medium","calculatorUse":null,"totalMarks":8,"questionType":"LA","isCalculation":true},{"id":"56a69fac-7065-42e6-b30b-a21da9d2291a","difficultyBand":"hard","calculatorUse":null,"totalMarks":8,"questionType":"LA","isCalculation":true},{"id":"598e1ee9-d7bd-4cb2-b9c6-3cc7d2b88479","difficultyBand":"medium","calculatorUse":null,"totalMarks":4,"questionType":"LA","isCalculation":true},{"id":"5a6268a5-821b-4c3a-bab2-6e2a22a7a517","difficultyBand":"medium","calculatorUse":null,"totalMarks":9,"questionType":"LA","isCalculation":true},{"id":"628b555b-bb68-4df3-9cd9-fee55098c4c7","difficultyBand":"medium","calculatorUse":null,"totalMarks":4,"questionType":"LA","isCalculation":false},{"id":"652a6a94-778e-4806-83a1-f819e484bd63","difficultyBand":"medium","calculatorUse":null,"totalMarks":13,"questionType":"LA","isCalculation":true},{"id":"6adf6f31-c479-4a97-be09-59b1a6274d5e","difficultyBand":"medium","calculatorUse":null,"totalMarks":3,"questionType":"LA","isCalculation":true},{"id":"6b1223c3-3eb3-46d9-b189-b43dfd983e74","difficultyBand":"hard","calculatorUse":null,"totalMarks":12,"questionType":"LA","isCalculation":true},{"id":"6b954785-9939-4c7a-8aee-da66f1badd78","difficultyBand":"medium","calculatorUse":null,"totalMarks":6,"questionType":"LA","isCalculation":true},{"id":"73b41449-59ac-497d-b487-09e0a816019d","difficultyBand":"medium","calculatorUse":null,"totalMarks":9,"questionType":"LA","isCalculation":true},{"id":"759efce3-6e85-4bbf-929b-b70be8027d21","difficultyBand":"medium","calculatorUse":null,"totalMarks":6,"questionType":"LA","isCalculation":true},{"id":"763347ec-121f-4b55-9b63-860c6d3642f6","difficultyBand":"medium","calculatorUse":null,"totalMarks":12,"questionType":"LA","isCalculation":true},{"id":"78af2a84-ceb2-4c9d-9d0b-4ae3a8ed8002","difficultyBand":"hard","calculatorUse":null,"totalMarks":7,"questionType":"LA","isCalculation":true},{"id":"796fbdfc-a7ed-4e53-9286-f64f4cbe4be0","difficultyBand":"medium","calculatorUse":null,"totalMarks":7,"questionType":"LA","isCalculation":true},{"id":"798c117d-a4ff-46de-9f87-692828cce780","difficultyBand":"medium","calculatorUse":null,"totalMarks":4,"questionType":"LA","isCalculation":false},{"id":"8081a7a9-df9b-4bc0-8590-005b14d95fad","difficultyBand":"medium","calculatorUse":null,"totalMarks":7,"questionType":"LA","isCalculation":true},{"id":"80c675ae-c5ac-4028-bbcb-8b3db75a14e3","difficultyBand":"medium","calculatorUse":null,"totalMarks":6,"questionType":"LA","isCalculation":true},{"id":"84771432-d7ab-4616-a6fd-f37a50e9269a","difficultyBand":"medium","calculatorUse":null,"totalMarks":5,"questionType":"LA","isCalculation":true},{"id":"8a04521d-d353-4863-a62c-b9d222433207","difficultyBand":"medium","calculatorUse":null,"totalMarks":9,"questionType":"LA","isCalculation":true},{"id":"8be4d94b-4507-4383-a2e8-d5f033fe8d02","difficultyBand":"medium","calculatorUse":null,"totalMarks":4,"questionType":"LA","isCalculation":true},{"id":"8ebc1394-5cdb-455f-a25d-6766c150b7ba","difficultyBand":"medium","calculatorUse":null,"totalMarks":4,"questionType":"LA","isCalculation":false},{"id":"9194ab18-af68-4117-9364-857f07b038d6","difficultyBand":"medium","calculatorUse":null,"totalMarks":8,"questionType":"LA","isCalculation":true},{"id":"996b6abb-4baf-4275-81ff-b0ab4e73b948","difficultyBand":"medium","calculatorUse":null,"totalMarks":9,"questionType":"LA","isCalculation":true},{"id":"9f7a597b-2efe-49fd-9dea-4ad2b141f46a","difficultyBand":"medium","calculatorUse":null,"totalMarks":5,"questionType":"LA","isCalculation":true},{"id":"a1d2b6ec-df5d-4f7b-8c86-c5b92bb30c67","difficultyBand":"medium","calculatorUse":null,"totalMarks":12,"questionType":"LA","isCalculation":true},{"id":"a5d0259a-5cec-41be-8f52-aa5683a79640","difficultyBand":"hard","calculatorUse":null,"totalMarks":8,"questionType":"LA","isCalculation":true},{"id":"b0d0eb60-ceb7-491d-9ba2-818dd9ecc01f","difficultyBand":"medium","calculatorUse":null,"totalMarks":4,"questionType":"LA","isCalculation":true},{"id":"b3657bab-3488-4ffa-af71-3222ec757ec3","difficultyBand":"medium","calculatorUse":null,"totalMarks":7,"questionType":"LA","isCalculation":true},{"id":"c0383345-f45a-48b6-851c-44384d7b70af","difficultyBand":"medium","calculatorUse":null,"totalMarks":8,"questionType":"LA","isCalculation":true},{"id":"c1732402-391b-4494-bb07-bd46da4fefd8","difficultyBand":"medium","calculatorUse":null,"totalMarks":8,"questionType":"LA","isCalculation":true},{"id":"c195ba73-d6c6-44d2-bfec-b1de4ca40f43","difficultyBand":"medium","calculatorUse":null,"totalMarks":3,"questionType":"LA","isCalculation":true},{"id":"c4de9f01-a6cf-4c42-9b37-8afacaa79009","difficultyBand":"medium","calculatorUse":null,"totalMarks":6,"questionType":"LA","isCalculation":true},{"id":"ccae4139-d718-4443-8d1b-9e52e56a46fe","difficultyBand":"medium","calculatorUse":null,"totalMarks":4,"questionType":"LA","isCalculation":true},{"id":"d5404ddf-d8b4-40da-8504-5e685b72f033","difficultyBand":"medium","calculatorUse":null,"totalMarks":15,"questionType":"LA","isCalculation":true},{"id":"d78e5e76-d516-4aec-8878-4041448d7b0c","difficultyBand":"hard","calculatorUse":null,"totalMarks":16,"questionType":"LA","isCalculation":true},{"id":"d7bd8e35-574c-417c-a496-2a4fd65a31bb","difficultyBand":"medium","calculatorUse":null,"totalMarks":8,"questionType":"LA","isCalculation":true},{"id":"d8ad0c4f-6e4d-4583-8c69-f6861081409f","difficultyBand":"medium","calculatorUse":null,"totalMarks":6,"questionType":"LA","isCalculation":true},{"id":"dcfda464-e53d-480a-aeb3-72da124a9328","difficultyBand":"medium","calculatorUse":null,"totalMarks":8,"questionType":"LA","isCalculation":true},{"id":"e047463f-0116-46f2-923d-bf5d49edd6dd","difficultyBand":"medium","calculatorUse":null,"totalMarks":9,"questionType":"LA","isCalculation":true},{"id":"e58aec50-421e-40be-be56-1cd58c1a7a40","difficultyBand":"medium","calculatorUse":null,"totalMarks":4,"questionType":"LA","isCalculation":false},{"id":"e6789c8e-b45a-4317-ad00-f16d2eb6fef6","difficultyBand":"medium","calculatorUse":null,"totalMarks":11,"questionType":"LA","isCalculation":true},{"id":"e79c5d66-d3a4-4787-9db4-a8bda6f14225","difficultyBand":"medium","calculatorUse":null,"totalMarks":5,"questionType":"LA","isCalculation":true},{"id":"e963c301-9c90-428f-8a7e-ce3d26f8289c","difficultyBand":"hard","calculatorUse":null,"totalMarks":13,"questionType":"LA","isCalculation":true},{"id":"ec691163-01bf-44ff-9d8e-59875ab7ab0a","difficultyBand":"medium","calculatorUse":null,"totalMarks":9,"questionType":"LA","isCalculation":true},{"id":"f7149f7f-7220-42ba-9038-4fa003ccad8e","difficultyBand":"medium","calculatorUse":null,"totalMarks":6,"questionType":"LA","isCalculation":true},{"id":"f741e45a-3beb-4b3f-8712-14a39d812f97","difficultyBand":"hard","calculatorUse":null,"totalMarks":13,"questionType":"LA","isCalculation":true},{"id":"f7c42d77-ed0f-4ad7-8c97-750efd22a0ad","difficultyBand":"medium","calculatorUse":null,"totalMarks":7,"questionType":"LA","isCalculation":true},{"id":"fa743f27-2376-494d-9fc2-c1fba6d45d81","difficultyBand":"medium","calculatorUse":null,"totalMarks":4,"questionType":"LA","isCalculation":false},{"id":"fa7bf159-3159-46a7-8020-178fbdeb932f","difficultyBand":"medium","calculatorUse":null,"totalMarks":10,"questionType":"LA","isCalculation":true},{"id":"fa9f5fd2-5fe2-4b80-a97b-04003fe5fa85","difficultyBand":"medium","calculatorUse":null,"totalMarks":10,"questionType":"LA","isCalculation":true},{"id":"fba3da4f-236e-45d8-8621-12a01c3e99d3","difficultyBand":"medium","calculatorUse":null,"totalMarks":4,"questionType":"LA","isCalculation":true}],"title":"1.10.4 Product, quotient and chain rules (A-level only)","topicId":"bb070e83-5617-4b2d-a167-e007ba2a6d42","topicSidebar":"$L3d","topicSlug":"product-quotient-and-chain-rules","topicTitle":"1.10.4 Product, quotient and chain rules (A-level only)"}]}],"$L3e","$L3f"]}]