# How do you find the derivative of 5e^x sqrt(x)?

Mar 10, 2015

I would use the Product Rule where if you have:

$y = f \left(x\right) g \left(x\right)$ then
$y ' = f ' \left(x\right) g \left(x\right) + f \left(x\right) g ' \left(x\right)$

$y ' = 5 {e}^{x} \sqrt{x} + 5 {e}^{x} \frac{1}{2 \sqrt{x}}$
$= 5 {e}^{x} \left[\sqrt{x} + \frac{1}{2 \sqrt{x}}\right] =$
$= 5 {e}^{x} \left[\frac{2 x + 1}{2 \sqrt{x}}\right]$
It is a good idea, after you memorize the first derivative rules, to memorize: $\frac{d}{\mathrm{dx}} \left(\sqrt{x}\right) = \frac{1}{2 \sqrt{x}}$.