Chapter 2 - Derivatives - 2.6 Implicit Differentiation - 2.6 Exercises - Page 166: 6

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

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