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7 marksDifferentiation II

CAPE Pure Mathematics Unit 2 · May/June 2008 (T&T) · Paper 2 · Question 1(b)

Given that u = e^{2x} + e^{-2x} and v = e^{2x} - e^{-2x}, show that \frac{\mathrm{d}^2u}{\mathrm{d}x^2} + \frac{\mathrm{d}^2v}{\mathrm{d}x^2} = 2\left(\frac{\mathrm{d}u}{\mathrm{d}x} + \frac{\mathrm{d}v}{\mathrm{d}x}\right).

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Other parts of this question

  1. 1(a)Find the exact values of x such that e^x + 7e^{-x} = 8.[5 marks]
  2. 1(c)(i)Differentiate (x \ln x) \sin^{-1} 2x with respect to x.[4 marks]
  3. 1(c)(ii)a)Show that \frac{\mathrm{d}y}{\mathrm{d}x} = t + \frac{1}{t}.[3 marks]
  4. 1(c)(ii)b)Show that C has points of inflexion at (8, 8) and (8, -8).[6 marks]

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