What is the derivative of sqrt(5x)?

Jul 12, 2016

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

or

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

Explanation:

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

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

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

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

$= \frac{5}{2} \cdot \frac{1}{\sqrt{5 x}}$

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

or

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