A chemical reaction's equilibrium state is represented by a curve CCC with the equation
2x−xy+y2=28,y≥0 2^x - xy + y^2 = 28, \quad y \ge 0 2x−xy+y2=28,y≥0where xxx and yyy represent the concentrations of two specific reagents in mol dm−3^{-3}−3. A specific experimental state PPP lies on CCC where the concentration x=4x = 4x=4.
Find the concentration yyy at state PPP.
Find dydx\frac{\text{d}y}{\text{d}x}dxdy in terms of xxx and yyy.
The tangent to CCC at PPP intersects the xxx-axis at the point QQQ.
Find the xxx-coordinate of QQQ, giving your answer in the form aln2+bcln2+d\frac{a \ln 2 + b}{c \ln 2 + d}cln2+daln2+b where a,b,ca, b, ca,b,c and ddd are integers to be found.
Practise AQA A Level Maths 1.10 G: Differentiation with exam-style questions for A Level Maths. 321 questions covering 1.10.1 The derivative and second derivative, 1.10.2 Differentiating standard functions, 1.10.3 Applications of differentiation, 1.10.4 Product, quotient and chain rules (A-level only), 1.10.5 Implicit and parametric differentiation (A-level only), and 1.10.6 Constructing differential equations (A-level only), matched to the AQA A Level Maths (7357) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.
