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6 marksDifferentiation II

CAPE Pure Mathematics Unit 2 · May/June 2024 · Paper 2 · Question 1(a)

This section covers Analysis, Matrices, and Complex Numbers. Module 1 focuses on Analysis.

Given that 3y² - 4xy + sin xy = 5, determine dy/dx.

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Other parts of this question

  1. 1(b)Differentiate cos⁻¹ (3x - 2), expressing your answer in its simplest form.[3 marks]
  2. 1(c)(i)Use partial fractions to show that (2x+1)/(3x²-x-2) = 3/(5(x-1)) + 1/(5(3x+2)).[7 marks]
  3. 1(c)(ii)Hence, or otherwise, determine ∫ (2x+1)/(3x²-x-2) dx.[4 marks]
  4. 1(d)Given that x = 2t - sin t and y = 1 - cos t, determine d²y/dx².[5 marks]

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