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

Mar 14, 2018

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

#### Explanation:

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

We need to use the chain rule:

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

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

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