Answer
See the attachment.
Work Step by Step
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.
