Answer
$\dfrac{y e^x}{y^3e^y +2 e^x}$
Work Step by Step
We have: $\dfrac{e^x}{y^2}=1+e^y$
We differentiate both sides with respect to $t$.
$-2y^{-3} \dfrac{dy}{dx}+y^{-2} e^x =e^y \dfrac{dy}{dx} \\ (e^y +2y^{-3} e^x)\dfrac{dy}{dx}=y^{-2} e^x\\\dfrac{dy}{dx}=\dfrac{y^{-2} e^x}{e^y +2y^{-3} e^x}$
Therefore, $ \dfrac{dy}{dx}=\dfrac{y e^x}{y^3e^y +2 e^x}$
