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1.10 G: Differentiation

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Question 127

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

1.10 G: Differentiation Questions

  1. A Level
  2. /Maths
  3. /1.10 G: Differentiation

375 exam-style questions on AQA A Level Maths 1.10 G: Differentiation, covering 1.10.1 The derivative and second derivative, 1.10.2 Differentiating standard functions, 1.10.3 Applications of differentiation, 1.10.4 Product, quotient and chain rules (A-level only), 1.10.5 Implicit and parametric differentiation (A-level only), and 1.10.6 Constructing differential equations (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

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