# How do you find the derivative of  2e^(4x^2)?

Jul 23, 2016

$f ' \left(x\right) = 16 x {e}^{4 {x}^{2}}$

#### Explanation:

$y = 2 {e}^{4 {x}^{2}}$

We need to use the chain rule as we have $y \left(u \left(x\right)\right)$.

$\frac{\mathrm{dy}}{\mathrm{dx}} = \frac{\mathrm{dy}}{\mathrm{du}} \frac{\mathrm{du}}{\mathrm{dx}}$

$u = 4 {x}^{2} \implies \frac{\mathrm{du}}{\mathrm{dx}} = 8 x$

$\frac{\mathrm{dy}}{\mathrm{du}} = \frac{d}{\mathrm{du}} \left(2 {e}^{u}\right) = 2 {e}^{u} = 2 {e}^{4 {x}^{2}}$

Hence

$\frac{\mathrm{dy}}{\mathrm{dx}} = 2 {e}^{4 {x}^{2}} \cdot 8 x = 16 x {e}^{4 {x}^{2}}$