Answer
$4(x+\sin x)^{3}(1+\cos x)$
Work Step by Step
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
$\frac{dy}{dx}=\frac{dy}{du}\times\frac{du}{dx}=\frac{d}{du}(u^{4})\times\frac{d}{dx}(x+\sin x)$
$=4u^{3}\times(1+\cos x)$
$=4(x+\sin x)^{3}(1+\cos x)$
