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Exam-Style Question on Differentiation

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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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The exam-style questions appearing on this site are based on those set in previous examinations (or sample assessment papers for future examinations) by the major examination boards. The wording, diagrams and figures used in these questions have been changed from the originals so that students can have fresh, relevant problem solving practice even if they have previously worked through the related exam paper.

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