327. Find $\left(\cos ^{3} x\right)^{\prime}$.
Solution. Here $u=\cos x, y=u^{3}$. We find $y_{u}^{\prime}=3 u^{2}=3 \cos ^{2} x$, $u_{x}^{\prime}=(\cos x)^{\prime}=-\sin x$; hence $y_{x}^{\prime}=3 \cos ^{2} x(-\sin x)=-3 \cos ^{2} x \sin x$.