# How do you implicitly differentiate x^2+ 2xy- y^2 + x=2?

Aug 14, 2015

${x}^{2}$+2xy−${y}^{2}$+x=2

To differentiate 2xy use product rule

2x + 2x.$\frac{\mathrm{dy}}{\mathrm{dx}}$ + 2y.1 - 2y$\frac{\mathrm{dy}}{\mathrm{dx}}$ + 1 = 0

Rewrite it

2x.$\frac{\mathrm{dy}}{\mathrm{dx}}$ - 2y$\frac{\mathrm{dy}}{\mathrm{dx}}$ + 2x + 2y + 1 = 0

2x.$\frac{\mathrm{dy}}{\mathrm{dx}}$ - 2y$\frac{\mathrm{dy}}{\mathrm{dx}}$ = - 2x - 2y - 1

$\frac{\mathrm{dy}}{\mathrm{dx}}$(2x - 2y) = - 2x - 2y - 1

$\frac{\mathrm{dy}}{\mathrm{dx}}$ = $\frac{- 2 x - 2 y - 1}{2 x - 2 y}$