If $x^2+xy+y^2=7$ defines $y$ implicitly as a function of $x$, then $\dfrac{dy}{dx}=$

Core Concept

Differentiating gives $2x+y+x\frac{dy}{dx}+2y\frac{dy}{dx}=0$. Collect the $\frac{dy}{dx}$ terms and solve to get $-\frac{2x+y}{x+2y}$.