Answer
$y'=4(x^{2}+x^{3})^{3}(2x+3x^{2})$
Work Step by Step
Start with function: $y=(x^{2}+x^{3})^{4}$.
Let $u = x^{2}+x^{3}$.
Substitute u into function: $y=u^{4}$.
Differentiate using power rule: $y' = 4u^{3}u'$.
$u'=2x+3x^{2}$.
Substitute values for $u$ and $u'$ back into equation to arrive at the answer:
$y'=4(x^{2}+x^{3})^{3}(2x+3x^{2})$.
