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

Renaming $u = 1 + {x}^{2}$, we can use the chain rule, which states that $\frac{\mathrm{dy}}{\mathrm{dx}} = \frac{\mathrm{dy}}{\mathrm{du}} \frac{\mathrm{du}}{\mathrm{dx}}$
Also, we can rewrite $\frac{1}{u}$ as ${u}^{-} 1$, following the rule of negative exponentials: ${a}^{-} n = \frac{1}{a} ^ n$
$\frac{\mathrm{dy}}{\mathrm{dx}} = - {u}^{-} 2 \left(2 x\right)$
Substituting $u$:
$\frac{\mathrm{dy}}{\mathrm{dx}} = - {\left(1 + {x}^{2}\right)}^{2} \left(2 x\right) = - \frac{2 x}{1 + {x}^{2}} ^ 2$