## Calculus (3rd Edition)

$4(x+\sin x)^{3}(1+\cos x)$
Let $g(x)=u=x+\sin x$ and $f(g(x))=y=(x+\sin x)^{4}=u^{4}$ Then, using the chain rule, we have $\frac{dy}{dx}=\frac{dy}{du}\times\frac{du}{dx}=\frac{d}{du}(u^{4})\times\frac{d}{dx}(x+\sin x)$ $=4u^{3}\times(1+\cos x)$ $=4(x+\sin x)^{3}(1+\cos x)$