Question

Find dy, dx for x^2 − y^2 = xy.

Answer 1

$\bf x^2-y^2=xy\implies \stackrel{\textit{using \underline{implicit differentiation}}}{2x-\stackrel{\textit{chain rule}}{2y\cfrac{dy}{dx}}=\stackrel{\textit{product rule}}{1y+x\cfrac{dy}{dx}}}\implies 2x-2y\cfrac{dy}{dx}=y+x\cfrac{dy}{dx} \\\\\\ 2x-y=x\cfrac{dy}{dx}+2y\cfrac{dy}{dx}\implies 2x-y=\cfrac{dy}{dx}(2+2y)\implies \cfrac{2x-y}{2+2y}=\cfrac{dy}{dx}$