How do you find the derivative of 1/(x+1)?

Jul 19, 2016

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

Explanation:

let's be different and write it as $\frac{d}{\mathrm{dx}} {\left(1 + x\right)}^{- 1}$ and use power rule and chain rule:

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

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

$= - {\left(1 + x\right)}^{- 2} \left(1\right)$

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