# How do you implicitly differentiate -10=x^2-y^2?

$\frac{\mathrm{dy}}{\mathrm{dx}} = \frac{x}{y}$
$\frac{d}{\mathrm{dx}} \left[- 10 = {x}^{2} - {y}^{2}\right] \Rightarrow 0 = 2 x - 2 y \left[\frac{\mathrm{dy}}{\mathrm{dx}}\right] \Rightarrow 2 x = 2 y \left[\frac{\mathrm{dy}}{\mathrm{dx}}\right] \Rightarrow \frac{\mathrm{dy}}{\mathrm{dx}} = \frac{x}{y}$