What is the derivative of sqrt(3x)?

Feb 12, 2016

sqrt(3)/(2sqrt(x)

Explanation:

If $y = \sqrt{3 x}$

$\frac{\mathrm{dy}}{\mathrm{dx}} = \frac{d \left(\sqrt{3} \cdot \sqrt{x}\right)}{\mathrm{dx}}$

$\textcolor{w h i t e}{\text{XXX}} = \sqrt{3} \cdot \frac{d \sqrt{x}}{\mathrm{dx}}$

$\textcolor{w h i t e}{\text{XXX}} = \sqrt{3} \cdot \frac{{\mathrm{dx}}^{\frac{1}{2}}}{\mathrm{dx}}$

$\textcolor{w h i t e}{\text{XXX}} = \sqrt{3} \cdot \frac{1}{2} {x}^{- \frac{1}{2}}$

$\textcolor{w h i t e}{\text{XXX}} = \sqrt{3} \cdot \frac{1}{2 \sqrt{x}}$