# How do you differentiate f(x)= x/(x^2+1)?

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