Question

Find dy/dx by implicit differentiation for x – y = xy.

Answer 1

$\bf x-y=xy\impliedby \textit{product rule on the right-hand-side} \\\\\\ 1-\cfrac{dy}{dx}=1\cdot y+x\cdot \cfrac{dy}{dx}\implies 1-\cfrac{dy}{dx}=y+x \cfrac{dy}{dx} \\\\\\ 1-y=\cfrac{dy}{dx}+x\cfrac{dy}{dx}\impliedby \textit{now, we take common factor} \\\\\\ 1-y=\cfrac{dy}{dx}(1+x)\implies \cfrac{1-y}{1+x}=\cfrac{dy}{dx}$