# What is the derivative of  x^2/(x^2 +3)?

Jun 24, 2016

$\frac{d}{\mathrm{dx}} \left({x}^{2} / \left({x}^{2} + 3\right)\right) = \frac{6 x}{{x}^{2} + 3} ^ 2$

#### Explanation:

Using a combination of the chain rule and power rule, we have:

$\frac{d}{\mathrm{dx}} {\left(u \left(x\right)\right)}^{n} = n {\left(u \left(x\right)\right)}^{n - 1} u ' \left(x\right)$

Hence:

$\frac{d}{\mathrm{dx}} \left({x}^{2} / \left({x}^{2} + 3\right)\right) = \frac{d}{\mathrm{dx}} \left(\frac{\left({x}^{2} + 3\right) - 3}{{x}^{2} + 3}\right)$

$\textcolor{w h i t e}{00} = \frac{d}{\mathrm{dx}} \left(1 - 3 {\left({x}^{2} + 3\right)}^{- 1}\right)$

$\textcolor{w h i t e}{00} = 0 - 3 \left(- 1\right) {\left({x}^{2} + 3\right)}^{- 2} \left(2 x\right)$

$\textcolor{w h i t e}{00} = \frac{6 x}{{x}^{2} + 3} ^ 2$