Answer
$\dfrac{dy}{dx}=\dfrac{e^x -2xe^y }{x^2e^y -2y}$
Work Step by Step
We have: $x^2e^y-y^2=e^x$
Apply Product Rule and chain rule and differentiate both sides with respect to $x$.
$x^2e^y \dfrac{dy}{dx}+e^y(2x) -2y \dfrac{dy}{dx}=e^x $
This implies that
$ (x^2e^y-2y) \dfrac{dy}{dx}=e^x -2xe^y $
Therefore, $\dfrac{dy}{dx}=\dfrac{e^x -2xe^y }{x^2e^y -2y}$
