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