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Paper 2 · June 2015 · Differentiation

Given that $y=e^{x}\sin x$ , find $\dfrac{d^{2}y}{dx^{2}}$ , giving your answer in its simplest form.

Model answer

$2e^{x}\cos x$

Also accepted: 2e^x cos x, 2e^{x}\cos x, 2e^xcosx

Explanation

By the product rule

\dfrac{dy}{dx}=e^{x}\sin x+e^{x}\cos x

. Differentiating again,

\dfrac{d^{2}y}{dx^{2}}=e^{x}\sin x+e^{x}\cos x+e^{x}\cos x-e^{x}\sin x=2e^{x}\cos x

.

Derived from ZIMSEC Mathematics Paper 2, June 2015, Q1

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