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 Edexcel A Level Maths Differentiation with exam-style questions for A Level Maths. 311 questions covering 9.1 Differentiating sin x and cos x, 9.2 Differentiating exponentials and logarithms, 9.3 The Chain Rule, 9.4 The Product Rule, 9.5 The Quotient Rule, 9.6 Differentiating Trigonometric Functions, 9.7 Parametric Differentiation, 9.8 Implicit Differentiation, 9.9 Using Second Derivatives, and 9.10 Rates of Change, matched to the Edexcel A Level Maths (9MA0) 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.
