# How do you find the derivative of 1/x?

Nov 23, 2016

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

#### Explanation:

We use the power rule for differentiation which is

$\frac{d}{\mathrm{dx}} \left({x}^{n}\right) = n {x}^{n - 1} \forall x \in \mathbb{R} , n \in \mathbb{R}$ where $n$ is constant

So,

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