# What is the derivative of 1/(1+x^4)?

Aug 26, 2016

$= - \frac{4 {x}^{3}}{1 + {x}^{4}} ^ \left(2\right)$

#### Explanation:

$\frac{d}{\mathrm{dx}} \frac{1}{1 + {x}^{4}}$

you might be tempted to use the quotient rule, which is fine but out of personal preference, i would write it as this

$\frac{d}{\mathrm{dx}} \left({\left(1 + {x}^{4}\right)}^{- 1}\right)$

...and use the power and chain rules

so
$\frac{d}{\mathrm{dx}} \left({\left(1 + {x}^{4}\right)}^{- 1}\right)$

$= - 1 {\left(1 + {x}^{4}\right)}^{- 2} \frac{d}{\mathrm{dx}} \left({x}^{4}\right)$

$= - 1 {\left(1 + {x}^{4}\right)}^{- 2} 4 {x}^{3}$

$= - \frac{4 {x}^{3}}{1 + {x}^{4}} ^ \left(2\right)$