# Question #05c1d

Dec 15, 2017

$= {e}^{\sqrt{x}} / \left(2 \sqrt{x}\right)$

#### Explanation:

first, derivative of ${e}^{x}$ is ${e}^{x}$ proof

derivative of ${e}^{\sqrt{x}}$ is ${e}^{\sqrt{x}} \cdot \frac{d}{\mathrm{dx}} \left(\sqrt{x}\right)$ chain rule

$= {e}^{\sqrt{x}} \cdot \frac{d}{\mathrm{dx}} \left({x}^{\frac{1}{2}}\right)$

$= {e}^{\sqrt{x}} \cdot \left(\frac{1}{2} {x}^{- \frac{1}{2}}\right)$ power rule

$= {e}^{\sqrt{x}} / \left(2 \sqrt{x}\right)$