# How do you find the derivative of f(x) = x^(5/ 2) e^x ?

$f ' \left(x\right) = {x}^{\frac{5}{2}} {e}^{x} + \frac{5}{2} {x}^{\frac{3}{2}} {e}^{x}$
Let $f = {x}^{\frac{5}{2}} , g = {e}^{x}$
$f ' = \frac{5}{2} {x}^{\frac{3}{2}} , g ' = {e}^{x}$
$f ' \left(x\right) = f g ' + g f '$
$f ' \left(x\right) = {x}^{\frac{5}{2}} {e}^{x} + \frac{5}{2} {x}^{\frac{3}{2}} {e}^{x}$