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Differentiation

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Question 112

A curve, CCC, has the equation 7sin⁡y+xcos⁡y=Ax7 \sin y + x \cos y = Ax7siny+xcosy=Ax where A A\,A is a constant. C C\,C passes through the point P(3,π3)\displaystyle P \left( \sqrt{3}, \frac{\pi}{3} \right)P(3​,3π​)

a.

Show that A=4A = 4A=4

[2]
b.

Show that dydx=4−cos⁡y7cos⁡y−xsin⁡y\displaystyle \frac{dy}{dx} = \frac{4 - \cos y}{7 \cos y - x \sin y}dxdy​=7cosy−xsiny4−cosy​

[5]
c.

Hence find the equation of the tangent to C C\,C at PPP.

[4]
Markscheme

Differentiation Questions

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

649 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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