# How do you find the derivative of 1/(x-5)?

Jan 4, 2016

Use $\frac{1}{a} = {a}^{-} 1$ and chain rule. It's $- \frac{1}{x - 5} ^ 2$

#### Explanation:

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

The chain rule:

$\left({\left(x - 5\right)}^{-} 1\right) ' = - 1 \cdot {\left(x - 5\right)}^{- 1 - 1} \cdot \left(x - 5\right) ' =$

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

Note: the chain rule does not make a difference in this case. However, if there was another function in which the denominator which didn't have a derivative equal to 1, the differentiation process would be more complex.