# How do you find the derivative of y=e^(2x^2+2x)?

Apr 14, 2018

$\frac{d}{\mathrm{dx}} {e}^{2 {x}^{2} + 2 x} = \left(4 x + 2\right) {e}^{2 {x}^{2} + 2 x}$

#### Explanation:

This problem will require an application of the Chain Rule which, when applied to $e$ raised to the power of some function $u ,$ tells us that

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

Here, $u = 2 {x}^{2} + 2 x ,$ so we have

$\frac{d}{\mathrm{dx}} {e}^{2 {x}^{2} + 2 x} = {e}^{2 {x}^{2} + 2 x} \cdot \frac{d}{\mathrm{dx}} \left(2 {x}^{2} + 2 x\right)$

$\frac{d}{\mathrm{dx}} \left(2 {x}^{2} + 2 x\right) = 4 x + 2$, so we end up with

$\frac{d}{\mathrm{dx}} {e}^{2 {x}^{2} + 2 x} = \left(4 x + 2\right) {e}^{2 {x}^{2} + 2 x}$