# How do you implicitly differentiate xy-1/y^2=22?

Dec 21, 2015

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

#### Explanation:

Start by differentiating both sides, bearing in mind that y is a function of x.

$\frac{d}{\mathrm{dx}} \left(x y - \frac{1}{y} ^ 2\right) = \frac{d}{\mathrm{dx}} 22$

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

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