Answer
See the attachment.
Work Step by Step
We are given:
$f(u)=u^{3/2}$, $g(x)=x^{4}+1$
The composite function is:
$f(g(x))=(x^{4}+1)^{3/2}$
Take the derivatives:
$f'(u)=\frac{3}{2}u^{\frac{1}{2}}$
$f'(g(x))=\frac{3}{2}(x^{4}+1)^{1/2}$
$g'(x)=4x^{3}$
$(f \circ g)'=f'(g(x))g'(x)$
$=\frac{3}{2}(x^{4}+1)^{1/2}\times 4x^{3}$
$=6x^{3}(x^{4}+1)^{1/2}$
See the filled table below.
