# What is the derivative of (x/(x^2+1))?

Jun 4, 2015

Using quotient rule, which states that for $y = f \frac{x}{g} \left(x\right)$,

$y ' = \frac{f ' \left(x\right) g \left(x\right) - f \left(x\right) g ' \left(x\right)}{g \left(x\right)} ^ 2$,

We can proceed to derivate this with no big problems.

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

$\frac{\mathrm{dy}}{\mathrm{dx}} = \frac{{x}^{2} + 1 - 2 {x}^{2}}{{x}^{2} + 1} ^ 2$

$\textcolor{g r e e n}{\frac{\mathrm{dy}}{\mathrm{dx}} = \frac{- {x}^{2} + 1}{{x}^{2} + 1} ^ 2}$