Question

differentiate tan[cos(sinx)]

Answer 1

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$\large -\frac{\cos(x)\sin(\sin(x))}{\left(\cos(\cos(\sin(x)))\right)^{\left(2\right)}}$

Answer 2

It can easily be differentiated using chain rule.

$\frac{d}{dx} ( \tan( \cos( \sin(x) ) )$

$= {sec}^{2} ( \cos( \sin(x) ). \frac{d}{dx} ( \cos( \sin(x) )$

$= {sec}^{2} ( \cos( \sin(x) ) .( - \sin( \sin(x) ) ). \frac{d}{dx} ( \sin(x) )$

$= {sec}^{2} \cos( \sin(x) ) .( - \sin( \sin(x) )). \cos(x)$