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5 marksDifferentiation II

CAPE Pure Mathematics Unit 2 · May/June 2008 (Rest of Region) · Paper 2 · Question 1(b)

Given y = 3^{-x}, show, by using logarithms, that \frac{\mathrm{d}y}{\mathrm{d}x} = -3^{-x} \ln 3.

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Other parts of this question

  1. 1(a)(i)Differentiate with respect to x: e^{4x} \cos(\pi x)[4 marks]
  2. 1(a)(ii)Differentiate with respect to x: \ln\left(\frac{x^2 + 1}{\sqrt{x}}\right)[4 marks]
  3. 1(c)(i)Express in partial fractions: \frac{2x^2 - 3x + 4}{(x - 1)(x^2 + 1)}[7 marks]
  4. 1(c)(ii)Hence, find \int \frac{2x^2 - 3x + 4}{(x - 1)(x^2 + 1)} \,\mathrm{d}x.[5 marks]

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