## anonymous 4 years ago given an implicit function y+xy+y ^{2}=2 how do you find its derivative..

Find the derivative with respect to x for each term, I'll show you we need to find dy/dx $\frac{d}{dx}( y+xy+ y^2)=\frac{d}{dx} (2)$ we get $\frac{dy}{dx}+y+x\frac{dy}{dx}+2y\frac{dy}{dx}=0$ now combine common terms $\frac{dy}{dx}(1+x+2y)+y=0$ $=> \frac{dy}{dx}(1+x+2y)=-y$ so we get $\frac{dy}{dx}=-\frac{y}{1+x+2y}$ The point to remember is to combine all dy/dx terms and then find dy/dx