Question

Find the derivative of xe power x sin x

Answer 1

Required Answer

Solution :

$\: \: \: \: \: \: \: \: \: \: \: \: \sf f(x) = \: x \: {e}^{x \sin( x)}$

$:\implies \sf {f}^{'} (x) = \frac{d}{dx} x \: {e}^{x \sin (x)}$

$: \implies \sf{f}^{'} (x) = \frac{d}{dx} \bigg(x \bigg) . {e}^{x \sin( x)} + x . \frac{d}{dx} \bigg( {e}^{ x \sin( x)} \bigg)$

$: \implies \sf {f}^{'} (x) = {e}^{x \: \sin( x)} + x .{e}^{x \: \sin( x)} \bigg( \sin( x) + x \cos(x) \bigg)$

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