#### Answer

$4x^{7}\left( 1+x\right) ^{3}\left( 2+3x\right) $

#### Work Step by Step

$y=\left( x^{2}+x^{3}\right) ^{4}\Rightarrow y'=4\times \left( x^{2}+x^{3}\right) ^{3}\times \dfrac {d}{dx}\left( x^{2}+x^{3}\right) =4\left( x^{2}+x^{3}\right) ^{3}\left( 2x+3x^{2}\right) =4x^{7}\left( 1+x\right) ^{3}\left( 2+3x\right) $