Answer
$\dfrac {1-2xy-y^{4}}{4xy^{3}+x^{2}-3} $
Work Step by Step
$xy^{4}+x^{2}y=x+3y\Rightarrow \dfrac {d}{dx}\left( xy^{4}\right) +\dfrac {d}{dx}\left( x^{2}y\right) =\dfrac {d}{dx}\left( x\right) +\dfrac {d}{dx}\left( 3y\right) \Rightarrow y^{4}+4xy^{3}\dfrac {dy}{dx}+2xy+x^{2}\dfrac {dy}{dx}=1+3\dfrac {dy}{dx}\Rightarrow \dfrac {dy}{dx}=\dfrac {1-2xy-y^{4}}{4xy^{3}+x^{2}-3} $
