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

Jul 4, 2016

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

#### Explanation:

As $f \left(x\right) = \frac{x}{{x}^{2} + 1}$, using quotient rule,

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

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

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