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9.8 Implicit Differentiation

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Question 23

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]

9.8 Implicit Differentiation Questions

  1. A Level
  2. /Maths
  3. /9.8 Implicit Differentiation

Practise Edexcel A Level Maths 9.8 Implicit Differentiation with exam-style questions for A Level Maths. 48 questions, matched to the Edexcel A Level Maths (9MA0) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.

Question bank