Suppose that $y$ is defined implicitly as a function $y(x)$ by an equation on the form $F(x,y)=0$. I'm trying to show that $\frac{dy}{dx}=-\frac{F_x(x,y)}{F_y(x,y)},$ but I don't know where to start. Can someone please give me a hint?
Both $y(x)$ and $F(x,y)$ are differentiable and $F_y(x,y)\neq 0$.