Question

Find dx/dy by implicit differentiation x^2=x+y/x−y

Answer 1

Answer:

${ \tt{ \frac{dy}{dx} ( {x}^{2}) = \frac{dy}{dx} ( \frac{x + y}{x - y}) }} \\ { \tt{2x = \frac{(x - y) \frac{dy}{dx} + (x + y) \frac{dy}{dx} }{ {(x - y)}^{2} } }} \\ { \tt{ \frac{dy}{dx}(2x) = 2x {(x - y)}^{2} }} \\ { \tt{ \frac{dy}{dx} = {(x - y)}^{2} }}$