# What is the derivative of x*x^(1/2)?

Dec 23, 2016

The derivative is $\frac{3}{2} \sqrt{x}$.
$x \cdot {x}^{\frac{1}{2}} = {x}^{1 + \frac{1}{2}} = {x}^{\frac{2}{2} + \frac{1}{2}} = {x}^{\frac{3}{2}}$.
The power rule states that $\frac{d}{\mathrm{dx}} \left({x}^{n}\right) = n {x}^{n - 1}$
$\frac{d}{\mathrm{dx}} \left({x}^{\frac{3}{2}}\right) = \frac{3}{2} {x}^{\frac{1}{2}} = \frac{3}{2} \sqrt{x}$