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

Jan 20, 2016

$\frac{1}{\sqrt{2 x}}$

#### Explanation:

rewrite $\sqrt{2 x} = {\left(2 x\right)}^{\frac{1}{2}}$

now differentiate using the 'chain rule '

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

$= \frac{1}{\sqrt{2 x}}$
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