# What is the derivative of 2 sqrtx ?

In general if $f \left(x\right) = a \cdot {x}^{b}$
$\textcolor{w h i t e}{\text{XXXX}}$$\frac{d f}{\mathrm{dx}} = b \cdot a \cdot {x}^{b - 1}$
Since $f \left(x\right) = 2 \sqrt{x}$
is the same as $f \left(x\right) = 2 \cdot {x}^{\frac{1}{2}}$
$\textcolor{w h i t e}{\text{XXXX}}$$\textcolor{w h i t e}{\text{XXXX}}$$\textcolor{w h i t e}{\text{XXXX}}$$\frac{d f}{\mathrm{dx}} = \left(\frac{1}{2}\right) \cdot 2 \cdot {x}^{- \frac{1}{2}}$
$\textcolor{w h i t e}{\text{XXXX}}$$\textcolor{w h i t e}{\text{XXXX}}$$\textcolor{w h i t e}{\text{XXXX}}$$\textcolor{w h i t e}{\text{XXXX}}$$= \frac{1}{\sqrt{x}}$