# What is the derivative of sqrt(5x+2)?

Oct 24, 2016

$\frac{5}{2 \sqrt{5 x + 2}}$

#### Explanation:

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

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

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

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