# How do you differentiate (5-x^-1)^(1/3)?

##### 1 Answer
Feb 10, 2015

You can use the Chain Rule.
You differentiate first the the $\frac{1}{3}$ power (leaving the argument as it is) and then multiply times the argument differentiated:

$\frac{1}{3} {\left(5 - {x}^{-} 1\right)}^{\frac{1}{3} - 1} \cdot {x}^{-} 2 =$

$\frac{1}{3} {\left(5 - {x}^{-} 1\right)}^{- \frac{2}{3}} \cdot {x}^{-} 2 =$

$= \frac{1}{3} \cdot \frac{1}{5 - {x}^{-} 1} ^ \left(\frac{2}{3}\right) \cdot \frac{1}{x} ^ 2$