# How do you find the derivative of 1/(x^2) - 1/x?

Jan 1, 2018

$- \frac{2}{x} ^ 3 + \frac{1}{x} ^ 2$

#### Explanation:

This can be done with the quotient rule, but the easiest thing to do is to first rewrite:

$\frac{1}{x} ^ 2 - \frac{1}{x} = {x}^{- 2} - {x}^{- 1}$

$\frac{d}{\mathrm{dx}} \left(\frac{1}{x} ^ 2 - \frac{1}{x}\right) = \frac{d}{\mathrm{dx}} \left({x}^{- 2} - {x}^{- 1}\right) = - 2 {x}^{- 3} - \left(- 1\right) {x}^{- 2}$
$= - \frac{2}{x} ^ 3 + \frac{1}{x} ^ 2$