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