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3.6 Differentiation (A-level only)

3.6 Differentiation (A-level only)

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Question 143

In a study of harmonic oscillations with variable frequency, the power P P\,P produced by a generator at time t t\,t is modeled by the equation

P=tcos⁡(3t)t>1,P>0 P = t^{\cos(3t)} \quad t > 1, \quad P > 0 P=tcos(3t)t>1,P>0
a.

Find, by firstly taking natural logarithms, an expression for dPdt\frac{dP}{dt}dtdP​ in terms of ttt and PPP.

[4]
b.

Hence show that the values of t t\,t for which the power is stationary are solutions of the equation

3tln⁡ttan⁡(3t)=1 3t \ln t \tan(3t) = 1 3tlnttan(3t)=1
[3]
Markscheme

3.6 Differentiation (A-level only) Questions

  1. A Level
  2. /Maths
  3. /3.6 Differentiation (A-level only)

333 exam-style questions on WJEC A Level Maths 3.6 Differentiation (A-level only), covering 3.6.1 Differentiation (A-level only), 3.6.2 Differentiation (A-level only), 3.6.3 Differentiation (A-level only), 3.6.4 Differentiation (A-level only), 3.6.5 Differentiation (A-level only), 3.6.6 Differentiation (A-level only), 3.6.7 Differentiation (A-level only), and 3.6 Differentiation (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

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