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

Oct 9, 2017

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

#### Explanation:

Right now, you have $y = {e}^{{x}^{2}}$

The derivative of $y = {e}^{f \left(x\right)}$ is $\frac{\mathrm{dy}}{\mathrm{dx}} = f ' \left(x\right) {e}^{f \left(x\right)}$

In this case, $f \left(x\right) = {x}^{2}$, and the derivative of ${x}^{2} = 2 x$

Therefore, $f ' \left(x\right) = 2 x$, and $\frac{\mathrm{dy}}{\mathrm{dx}} = 2 x {e}^{{x}^{2}}$