# How do you differentiate y = x / (x^2 + 3 )?

$\frac{\mathrm{dy}}{\mathrm{dx}} = \frac{3 - {x}^{2}}{{x}^{2} + 3} ^ 2$

#### Explanation:

Use the formula for derivatives of quotients

$\frac{d}{\mathrm{dx}} \left(\frac{u}{v}\right) = \frac{v \frac{\mathrm{du}}{\mathrm{dx}} - u \frac{\mathrm{dv}}{\mathrm{dx}}}{v} ^ 2$

Let $u = x$
Let $v = {x}^{2} + 3$

$\frac{\mathrm{dy}}{\mathrm{dx}} = \frac{\left({x}^{2} + 3\right) \cdot 1 - x \left(2 x\right)}{{x}^{2} + 3} ^ 2$

$\frac{\mathrm{dy}}{\mathrm{dx}} = \frac{3 - {x}^{2}}{{x}^{2} + 3} ^ 2$