Question

If $y={\cos }^{3}x$, then $\frac{dy}{dx}=$.

Answer 1

$Given:y={\cos }^{3}xByapplyingchainrule,letf=u^3,u=\cos xStep1:\frac{d}{du}{u}^3=3u^{2}Step2:\frac{d}{dx}\cos x=-\sin x=3u^2(-\sin x)[\because u=\cos x]=-3{\cos }^{2}x\sin xHence\frac{d}{dx}\left({\cos }^{3}x\right)=-3{\cos }^{2}x\sin x$