# How do you find the derivative of f(x)=1/(x+2)?

Apr 15, 2018

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

#### Explanation:

Let $g \left(x\right) = u$

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

Applying power rule,

$\text{ "d((u^-1))/dx=(-u^-2)(du)/dx" } \ldots \left(1\right)$

Here $u = \left(x + 2\right)$ and $\frac{\mathrm{du}}{\mathrm{dx}} = 1$

Plugging these in $\left(1\right)$, we get $\frac{d \left(\frac{1}{x + 2}\right)}{\mathrm{dx}} = - \frac{1}{x + 2} ^ 2$