#### Answer

For $2x^2+xy-y^2=2$ find $\frac{dy}{dx}$ by implicit differentiation
$\frac{dy}{dx}=\frac {-4x-y}{x-2y}$

#### Work Step by Step

Differentiate both sides with respect to x
$4x+y+x\frac{dy}{dx}-2y\frac{dy}{dx}=0$
Isolate $\frac{dy}{dx}$
$\frac{dy}{dx}(x-2y)=-4x-y$
$\frac{dy}{dx}=\frac {-4x-y}{x-2y}$