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Differentiation

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Question 597

The horizontal position x x\,x of a piston in a high-precision engine is modelled by the equation

x=18cos⁡2(2θ)0<θ<π4 x = 18 \cos^2(2\theta) \qquad 0 < \theta < \frac{\pi}{4} x=18cos2(2θ)0<θ<4π​

where θ \theta\,θ is the crankshaft angle in radians.

Show that the rate of change of the angle with respect to the position, dθdx\displaystyle \frac{d\theta}{dx}dxdθ​, can be expressed in the form

dθdx=−1ABx−x2 \frac{d\theta}{dx} = -\frac{1}{A\sqrt{Bx - x^2}} dxdθ​=−ABx−x2​1​

where A A\,A and B B\,B are integers to be determined.

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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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