# How do you find the derivative of sqrt (5x+2)?

Jan 31, 2016

$\frac{5}{2 {\left(5 x + 2\right)}^{\frac{1}{2}}}$

#### Explanation:

rewrite as ${\left(5 x + 2\right)}^{\frac{1}{2}}$

differentiate using$\textcolor{b l u e}{\text{ chain rule }}$

$\frac{d}{\mathrm{dx}} {\left(5 x + 2\right)}^{\frac{1}{2}} = \frac{1}{2} {\left(5 x + 2\right)}^{- \frac{1}{2}} \frac{d}{\mathrm{dx}} \left(5 x + 2\right)$

$= \frac{1}{2} {\left(5 x + 2\right)}^{- \frac{1}{2}} . 5$

$= \frac{5}{2} {\left(5 x + 2\right)}^{- \frac{1}{2}} = \frac{5}{2 {\left(5 x + 2\right)}^{\frac{1}{2}}}$