# How do you find the derivative of y=e^(3x+4)?

Apr 9, 2018

$3 {e}^{3 x + 4}$

#### Explanation:

Given: $y = {e}^{3 x + 4}$

Use the chain rule, which states that,

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

Let $u = 3 x + 4 , \therefore \mathrm{du} = 3 \setminus \mathrm{dx} , \frac{\mathrm{du}}{\mathrm{dx}} = 3$.

Here, $y = {e}^{u} , \therefore \mathrm{dy} = {e}^{u} \setminus \mathrm{du} , \frac{\mathrm{dy}}{\mathrm{du}} = {e}^{u}$.

Multiplying those results together, we get,

$\frac{\mathrm{dy}}{\mathrm{dx}} = {e}^{u} \cdot 3$

$= 3 {e}^{u}$

Substituting back $u = 3 x + 4$, we get,

$= 3 {e}^{3 x + 4}$