# What is the derivative of x + 1/x?

May 8, 2016

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

#### Explanation:

We will want to use the power rule, which states that the derivative of ${x}^{n}$ is $n {x}^{n - 1}$. We can make this rule apply by rewriting the given function:

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

Applying the power rule to both, we obtain the derivative:

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

$f ' \left(x\right) = 1 {x}^{0} - {x}^{-} 2$

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