# How do you use the quotient rule to differentiate f(x)=(x)/(x2+1)?

Sep 23, 2016

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

#### Explanation:

We have: $f \left(x\right) = \frac{x}{{x}^{2} + 1}$

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

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

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