# Derivative of f(x)=e^x^2?

Mar 29, 2018

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

#### Explanation:

We have a chain rule we have the outside function $f \left(u\right) = {e}^{u}$

and the inside function $u = {x}^{2}$

Chain rule is derive both functions and then multiply the derivatives

so $f ' \left(u\right) \cdot u '$

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

Mutply derivatives

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