What is the implicit derivative of 10=xy-y^2+x^2 ?

Apr 10, 2018

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

Explanation:

$10 = x y - {y}^{2} + {x}^{2}$

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

$0 = \left(x - 2 y\right) \times \frac{\mathrm{dy}}{\mathrm{dx}} + y + 2 x$

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