## Calculus (3rd Edition)

$-\sin x \sec^{2}(\cos x)$
$y= \tan(\cos x)$ Let $\cos x= t$ Then, $y= \tan t$. According to the chain rule, $\frac{dy}{dx}= \frac{dy}{dt}\cdot\frac{dt}{dx}$ Therefore, $\frac{dy}{dx}=\sec^{2}t\times-\sin x$ $=-\sin x \sec^{2}(\cos x)$