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

Dec 10, 2016

You have to use the chain rule: $f \left(g \left(x\right)\right) ' = f ' \left(g \left(x\right)\right) \cdot g ' \left(x\right)$

#### Explanation:

In this case $g \left(x\right) = {e}^{2 x} + 1$ , so we have:

$g ' \left(x\right) = 2 {e}^{2 x}$, again by the chain rule.

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

Putting it all together we have:

$3 {\left({e}^{2 x} + 1\right)}^{2} \cdot 2 {e}^{2 x} = 6 {\left({e}^{2 x} + 1\right)}^{2} \cdot {e}^{2 x}$