## Calculus (3rd Edition)

We are given: $f(u)=u^{4}+u$, $g(x)=\cos x$ The composite function is: $f(g(x))=(\cos x)^{4}+\cos x=\cos^{4}x+\cos x$ Take the derivatives: $f'(u)=4u^{3}+1$ $f'(g(x))=4(\cos x)^{3}+1= 4\cos^{3}x+1$ $g'(x)=-\sin x$ $(f \circ g)'=f'(g(x))g'(x)$ $= (4\cos^{3}x+1)\times -\sin x$. $=-\sin x(4\cos^{3}x+1)$ See the filled table below.