:"4df9831d-54c6-4f83-a597-6072e61bacd7","topicSlug":"differentiation-5","cards":[{"id":"6e4a82a7-4a5e-401d-a92f-d9da8015e48e","cardType":"basic","front":"What gives the gradient of a curve at a particular point?","back":"The gradient of the tangent at that point.","points":1,"mcqOptions":null},{"id":"4496ebd2-e662-43e6-9210-0bf45c5abfb0","cardType":"basic","front":"What does $f'(2)=5$ tell you about $y=f(x)$?","back":"At $x=2$, the curve has gradient 5.","points":1,"mcqOptions":null},{"id":"7159aa5d-6626-490c-be45-c7e8b9528b30","cardType":"cloze","front":"If $y=f(x)$, its derivative can be written $\\frac{dy}{dx}$ or $\\text{[...]}$.","back":"If $y=f(x)$, its derivative can be written $\\frac{dy}{dx}$ or $\\boxed{f'(x)}$.","points":null,"mcqOptions":null},{"id":"bb1b4fdf-aa5c-44cf-ab66-0c5be1f9f093","cardType":"cloze","front":"The original function gives the curve's height; its derivative gives the curve's [ ].","back":"The original function gives the curve's height; its derivative gives the curve's gradient.","points":null,"mcqOptions":null},{"id":"2a6b4ee7-1665-4e80-9fd5-317db1ccbc72","cardType":"basic","front":"Why is the derivative of a constant zero?","back":"Its graph is horizontal, so its gradient is zero.","points":2,"mcqOptions":null},{"id":"5059bbd1-f8bb-4a3b-b539-991c0875235c","cardType":"basic","front":"Rewrite $\\sqrt{x}$ in index form.","back":"$x^{\\frac12}$","points":1,"mcqOptions":null},{"id":"81e3fb7a-535b-4a19-87d3-35401f4ce134","cardType":"cloze","front":"A reciprocal power can be rewritten as $\\frac{1}{x^p}=$ $\\text{[...]}$.","back":"A reciprocal power can be rewritten as $\\frac{1}{x^p}=$ $\\boxed{x^{-p}}$.","points":null,"mcqOptions":null},{"id":"8069e1a6-5720-447b-b2f1-1dcf87f2948c","cardType":"cloze","front":"A general root can be rewritten as $\\sqrt[q]{x^p}=$ $\\text{[...]}$.","back":"A general root can be rewritten as $\\sqrt[q]{x^p}=$ $\\boxed{x^{\\frac{p}{q}}}$.","points":null,"mcqOptions":null},{"id":"87d532fc-2325-479c-9f7c-cad8e07a1e2b","cardType":"cloze","front":"For rational $n$, the power rule is $\\frac{d}{dx}(x^n)=$ $\\text{[...]}$.","back":"For rational $n$, the power rule is $\\frac{d}{dx}(x^n)=$ $\\boxed{nx^{n-1}}$.","points":null,"mcqOptions":null},{"id":"fe2f0b3f-32f0-403d-822d-dfb7c045f76a","cardType":"basic","front":"Differentiate $x^7$.","back":"$7x^6$","points":1,"mcqOptions":null},{"id":"dc13b9b0-12f1-4013-9a1c-a598c50de1ce","cardType":"basic","front":"Differentiate $ax^n$, where $a$ and $n$ are constants.","back":"$anx^{n-1}$","points":1,"mcqOptions":null},{"id":"56679cd5-d652-4b18-a5b1-91f741b78bf0","cardType":"basic","front":"Differentiate $x^{\\frac52}$.","back":"$\\frac52x^{\\frac32}$","points":2,"mcqOptions":null},{"id":"1d0e2824-95e9-41b2-b919-6e172d7df424","cardType":"basic","front":"Differentiate $x^{-2}$.","back":"$-2x^{-3}$","points":2,"mcqOptions":null},{"id":"845f2edb-28f3-496c-9714-0d736b879ba2","cardType":"basic","front":"Differentiate $7x$.","back":"$7$","points":1,"mcqOptions":null},{"id":"8fc543e1-6e94-48be-8ddf-298f6cfd77fb","cardType":"cloze","front":"When differentiating a sum or difference term by term, each term keeps its original [ ].","back":"When differentiating a sum or difference term by term, each term keeps its original sign.","points":null,"mcqOptions":null},{"id":"e7dd504d-78db-4ee6-98fe-e210ade700fe","cardType":"basic","front":"Differentiate $f(x)=3x^5-4x^3+7x-8$.","back":"$f'(x)=15x^4-12x^2+7$","points":3,"mcqOptions":null},{"id":"22791ce1-12a5-41c3-afd9-7

1.7.4 Differentiation Flashcards

1.7.4 Differentiation Flashcards