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3.5 Differentiation (A-level only)

3.5 Differentiation (A-level only)

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Question 124

A curve CCC has equation

y=xcos⁡xx>0,y>0 y = x^{\cos x} \quad x > 0, \quad y > 0 y=xcosxx>0,y>0
a.

Find, by firstly taking natural logarithms, an expression for dydx\frac{dy}{dx}dxdy​ in terms of xxx and yyy.

[4]
b.

Hence show that the xxx-coordinates of the stationary points of CCC are solutions of the equation

sin⁡(x)⋅xln⁡x=cos⁡x \sin(x) \cdot x \ln x = \cos x sin(x)⋅xlnx=cosx
[3]
Markscheme

3.5 Differentiation (A-level only) Questions

  1. A Level
  2. /Maths
  3. /3.5 Differentiation (A-level only)

263 exam-style questions on CCEA A Level Maths 3.5 Differentiation (A-level only), covering 3.5.1 Differentiation (A-level only), 3.5.2 Differentiation (A-level only), 3.5.3 Differentiation (A-level only), 3.5.4 Differentiation (A-level only), 3.5.5 Differentiation (A-level only), and 3.5 Differentiation (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

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