If $f(x)=\sin^2(\cos x)$, then $f'(x)=$

Core Concept

Layer the chain rule: the outer square gives $2\sin(\cos x)$, the derivative of $\sin u$ gives $\cos(\cos x)$, and the derivative of $\cos x$ is $-\sin x$. The product is $-2\sin x\sin(\cos x)\cos(\cos x)$.