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Differentiation

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Question 402

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

Differentiation Questions

  1. A Level
  2. /Maths
  3. /Differentiation

717 exam-style questions on Edexcel A Level Maths Differentiation, covering 9.1 Differentiating sin x and cos x, 9.2 Differentiating exponentials and logarithms, 9.3 The Chain Rule, 9.4 The Product Rule, 9.5 The Quotient Rule, 9.6 Differentiating Trigonometric Functions, 9.7 Parametric Differentiation, 9.8 Implicit Differentiation, 9.9 Using Second Derivatives, and 9.10 Rates of Change. Each one has a worked solution and a mark scheme showing where the marks go.

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