Answer
See the attachment.
Work Step by Step
We are given: $f(u)=\tan u$, $g(x)=x^{4}$
The composite function is:
$f(g(x))=\tan(x^{4})$
Take the derivatives:
$f'(u)=\sec^{2}u$
$f'(g(x))=\sec^{2} (x^{4})$
$g'(x)=4x^{3}$
$(f \circ g)'=f'(g(x))g'(x)$
$=\sec^{2}(x^{4})\times 4x^{3}$ $=4x^{3}\sec^{2}(x^{4})$
See the filled table below.
