Question

given an implicit function y+xy+y ^{2}=2 how do you find its derivative..

Answer 1

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