# Exam-Style Question on Differentiation

## A mathematics exam-style question with a worked solution that can be revealed gradually

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Question id: 402. This question is similar to one that appeared on an A-Level paper. The use of a calculator is allowed.

The following equation defines a curve which passes through $$A( 2 \pi ,3 \pi)$$

$$\sin 2y + y \cos^22x = x + c$$

(a) Find the exact value of the constant $$c$$.

(b) Find an expression for $$\frac{dy}{dx}$$

(c) Find the equation of the normal to the curve at A, giving your answer in the form $$y = mx + b$$

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