# How do you differentiate f(x)=((1/x)^2-x) using the chain rule?

May 23, 2017

$f ' \left(x\right) = - \frac{2}{x} - 1$

#### Explanation:

$f \left(x\right) = \left({\left(\frac{1}{x}\right)}^{2} - x\right)$

$= {x}^{-} 2 - x$

NB: Although the question calls for use of the chain rule, this is not applicable in this case. The derivative may be found by applying the power rule.

$f ' \left(x\right) = - 2 {x}^{-} 1 - 1$

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