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Differentiation

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Question 181

The intensity, III, of a specialized acoustic wave at a distance rrr from the source is modeled by the equation:

I=rsin⁡(2r),r>0,I>0 I = r^{\sin(2r)}, \quad r > 0, \quad I > 0 I=rsin(2r),r>0,I>0
a.

By first taking natural logarithms, find an expression for dIdr\frac{dI}{dr}drdI​ in terms of III and rrr.

[5]
b.

Hence show that at any stationary point of the intensity, the distance rrr must satisfy the equation:

tan⁡(2r)+2rln⁡r=0 \tan(2r) + 2r \ln r = 0 tan(2r)+2rlnr=0
[3]

Differentiation Questions

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

Practise Edexcel A Level Maths Differentiation with exam-style questions for A Level Maths. 311 questions 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, 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