# What is the derivative of e^((x^2)/2)?

Sep 28, 2016

$x {e}^{{x}^{2} / 2}$

#### Explanation:

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

Applying the chain rule:

$f ' \left(x\right) = {e}^{{x}^{2} / 2} \cdot \frac{d}{\mathrm{dx}} \left({x}^{2} / 2\right)$ Standard differential

$= {e}^{{x}^{2} / 2} \cdot \frac{2 x}{2}$ Power rule

$= x {e}^{{x}^{2} / 2}$