Answer
$\frac{dy}{dx}=-\sin x\cos (\cos x)$
Work Step by Step
Considering $u=\cos x$, the function can be written as $y=\sin(u)$.
We have $y=f(g(x))$ where $g(x)=\cos x$ and $f(u)=\sin(u)$.
Then,
$\frac{dy}{dx}=\frac{dy}{du}\cdot \frac{du}{dx}$ (By the chain rule)
$=\frac{d}{du}(\sin(u))\cdot \frac{d}{dx}(\cos x)$ (Use the derivative for trigonometric)
$=\cos (u)\cdot (-\sin x)$
$=\cos(\cos x)\cdot (-\sin x)$
$=-\sin x\cos (\cos x)$
Thus,
$\frac{dy}{dx}=-\sin x\cos (\cos x)$
