# What is the derivative of sqrt(4+x^2)?

Nov 12, 2016

$\frac{d}{\mathrm{dx}} \left(\sqrt{4 + {x}^{2}}\right) = \frac{x}{\sqrt{{x}^{2} + 4}}$

#### Explanation:

Rewrite this as ${\left(4 + {x}^{2}\right)}^{\frac{1}{2}}$ by properties of exponents.

Now use the chain rule to differentiate.

$\implies \left(\frac{1}{2}\right) {\left(4 + {x}^{2}\right)}^{- \frac{1}{2}} \left(2 x\right)$

$\implies x {\left(4 + {x}^{2}\right)}^{- \frac{1}{2}}$

This can also be written as $\frac{x}{\sqrt{4 + {x}^{2}}}$