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3 marksDifferentiation II

CAPE Pure Mathematics Unit 2 · May/June 2011 · Paper 2 · Question 1(b)(i)

Let y = x \sin \frac{1}{x}, x \neq 0.

Show that x \frac{dy}{dx} = y - \cos \left(\frac{1}{x}\right).

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Other parts of this question

  1. 1(a)(i)Find \frac{dy}{dx} if x^2 + y^2 - 2x + 2y - 14 = 0.[3 marks]
  2. 1(a)(ii)Find \frac{dy}{dx} if y = e^{\cos x}.[3 marks]
  3. 1(a)(iii)Find \frac{dy}{dx} if y = \cos^2 6x + \sin^2 8x.[3 marks]
  4. 1(b)(ii)Show that x^4 \frac{d^2y}{dx^2} + y = 0.[3 marks]
  5. 1(c)(i)Find the gradient of the tangent to the curve at the point where t = 4.[7 marks]
  6. 1(c)(ii)Find the equation of the tangent to the curve at the point where t = 4.[3 marks]

More practice: the rest of this paper · more Differentiation II questions · all CAPE Pure Mathematics Unit 2 past papers