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

Mar 27, 2015

For $f \left(x\right) = {e}^{2 {x}^{2}}$, the derivative is $f ' \left(x\right) = 4 x {e}^{2 {x}^{2}}$.

To get this answer, we use the fact that the exponential function is its own derivative, together with the chain rule:

For $f \left(x\right) = {e}^{g \left(x\right)}$, the derivative is: $f ' \left(x\right) = {e}^{g \left(x\right)} g ' \left(x\right)$,

In differential operator notation: $\frac{d}{\mathrm{dx}} \left({e}^{u}\right) = {e}^{u} \frac{\mathrm{du}}{\mathrm{dx}}$

For $f \left(x\right) = {e}^{2 {x}^{2}}$, the derivative is

$f ' \left(x\right) = {e}^{2 {x}^{2}} \cdot \left(4 x\right) = 4 x {e}^{2 {x}^{2}}$.