# How do you differentiate x^2 + 9y^2 = 1?

Sep 23, 2016

$\frac{\mathrm{dy}}{\mathrm{dx}} = - \frac{x}{9 y}$

#### Explanation:

${x}^{2} + 9 {y}^{2} = 1$

By implicit differentiation
$2 x + 9 \cdot 2 y \cdot \frac{\mathrm{dy}}{\mathrm{dx}} = 0$

$18 y \cdot \frac{\mathrm{dy}}{\mathrm{dx}} = - 2 x$

$\frac{\mathrm{dy}}{\mathrm{dx}} = - \frac{x}{9 y}$