# How do you implicitly differentiate 15=x^2/y+y^2?

Mar 18, 2018

$\frac{\mathrm{dy}}{\mathrm{dx}} = \frac{2 x}{15 - 3 {y}^{2}}$

#### Explanation:

$15 = {x}^{2} / y + {y}^{2}$ , Multiply both sides by $y$

$15 y = {x}^{2} + {y}^{3}$ and so differentiating implicitly with respect to $x$

$15 \frac{\mathrm{dy}}{\mathrm{dx}} = 2 x + 3 {y}^{2} \frac{\mathrm{dy}}{\mathrm{dx}}$

$15 \frac{\mathrm{dy}}{\mathrm{dx}} - 3 {y}^{2} \frac{\mathrm{dy}}{\mathrm{dx}} = 2 x$

$\frac{\mathrm{dy}}{\mathrm{dx}} \left[15 - 3 {y}^{2}\right] = 2 x$

$\frac{\mathrm{dy}}{\mathrm{dx}} = \frac{2 x}{15 - 3 {y}^{2}}$.