Question

Differentiate the given function w.r.t. $x$:
${\sin }^{3}x+{\cos }^{6}x$

Answer 1

Let $y={\sin }^{3}x+{\cos }^{6}x$
$\therefore \frac{dy}{dx}=\frac{d}{dx}\left({\sin }^{3}x\right)+\frac{d}{dx}\left({\cos }^{6}x\right)$
$=3{\sin }^{2}x.\frac{d}{dx}\left(\sin x\right)+6{\cos }^{5}x.\frac{d}{dx}\left(\cos x\right)$
$=3{\sin }^{2}x.\cos x+6{\cos }^{5}x.(-\sin x)$
$=3\sin x\cos x(\sin x-2{\cos }^{4}x)$