# How do you differentiate y= (e^2x + 1)^3?

Aug 13, 2015

Assuming that the function ought to be $y = {\left({e}^{2 x} + 1\right)}^{3}$, use the chain rule twice.

#### Explanation:

$y = {\left({e}^{2 x} + 1\right)}^{3}$

$\frac{\mathrm{dy}}{\mathrm{dx}} = 3 {\left({e}^{2 x} + 1\right)}^{2} \left[\frac{d}{\mathrm{dx}} \left({e}^{2 x} + 1\right)\right]$

$= 3 {\left({e}^{2 x} + 1\right)}^{2} \left[{e}^{2 x} \frac{d}{\mathrm{dx}} \left(2 x\right)\right]$

$= 3 {\left({e}^{2 x} + 1\right)}^{2} {e}^{2 x} 2$

$= 6 {e}^{2 x} {\left({e}^{2 x} + 1\right)}^{2}$