Derivative of $x \sin x$

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$x \cos x$

$x \sin x$

$x \cos x + \sin x$

$\sin x$

answer is C.

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Detailed Solution

We have, $\begin{array}{l} \frac{d}{d x} (x \sin x) = x \cdot \frac{d}{d x} (\sin x) + \sin x \cdot \frac{d}{d x} (x) \\ = x \cos x + \sin x \cdot 1 = x \cos x + \sin x . \end{array}$

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