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Differentiation

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Question 477

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≥0

where 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.

a.

Find the concentration yyy at state PPP.

[2]
b.

Find dydx\frac{\text{d}y}{\text{d}x}dxdy​ in terms of xxx and yyy.

[3]
c.

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 aln⁡2+bcln⁡2+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.

[4]
Markscheme

Differentiation Questions

  1. A Level
  2. /Maths
  3. /Differentiation

717 exam-style questions on Edexcel A Level Maths Differentiation, 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. Each one has a worked solution and a mark scheme showing where the marks go.

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