# How do you find the derivative of y=1/x^2?

Jan 14, 2016

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

#### Explanation:

The derivative of $y = a {x}^{n}$

is $\frac{\mathrm{dy}}{\mathrm{dx}} = n a {x}^{n - 1}$

By rewriting $y = \frac{1}{x} ^ 2$ as $y = {x}^{- 2}$

then it is in the form $a {x}^{n}$

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