Find the derivative of $y = (2 - x^{2}) cos x + 2 x sin x$

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Solution

$y = (2 - x^{2}) cos x + 2 x sin x$
$y = 2 cos x - x^{2} cos x + 2 x sin x$
$\frac{d y}{d x} = - 2 sin x - [x^{2} (- sin x) + cos x (2 x)] + 2 [x cos x + sin x]$
$= - 2 sin x + x^{2} sin x - 2 x cos x + 2 x cos x + 2 sin x$
$= x^{2} sin x$ .

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