# What is the derivative of sqrt(x^3)?

$f \left(x\right) = \sqrt{{x}^{3}} = {\left({x}^{3}\right)}^{\frac{1}{2}}$
$f ' \left(x\right) = \frac{1}{2} {\left({x}^{3}\right)}^{- \frac{1}{2}} 3 {x}^{2} = \left(\frac{3}{2} {x}^{2}\right) \left({x}^{- \frac{3}{2}}\right) = \frac{3}{2} {x}^{2 - \frac{3}{2}} = \frac{3}{2} {x}^{\frac{1}{2}} = \frac{3 \sqrt{x}}{2}$