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

Apr 1, 2018

$\frac{d}{\mathrm{dx}} {e}^{{x}^{2}} = 2 x {e}^{{x}^{2}}$

#### Explanation:

In general, when applying the Chain Rule to the exponential,

$\frac{d}{\mathrm{dx}} {e}^{u} = {e}^{u} \frac{\mathrm{du}}{\mathrm{dx}}$.

Here, $u = {x}^{2} ,$ so

$\frac{d}{\mathrm{dx}} {e}^{{x}^{2}} = {e}^{{x}^{2}} \frac{d}{\mathrm{dx}} {x}^{2}$

$\frac{d}{\mathrm{dx}} {e}^{{x}^{2}} = 2 x {e}^{{x}^{2}}$