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

Feb 15, 2018

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

#### Explanation:

Using the chain rule:

$\frac{d}{\mathrm{dx}} f \left(y \left(x\right)\right) = \frac{\mathrm{df}}{\mathrm{dy}} \times \frac{\mathrm{dy}}{\mathrm{dx}}$

with $y = \sqrt{x}$:

$\frac{d}{\mathrm{dx}} \left({e}^{\sqrt{x}}\right) = \left(\frac{d}{\mathrm{dy}} {e}^{y}\right) \left(\frac{d}{\mathrm{dx}} \sqrt{x}\right)$

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

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