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

Sep 8, 2014

By Chain Rule,
$y ' = 2 {e}^{2 x}$

Recall:
$\left({e}^{x}\right) ' = {e}^{x}$
Chain Rule: $\left[f \left(g \left(x\right)\right)\right] ' = f ' \left(g \left(x\right)\right) \cdot g ' \left(x\right)$

In the posted problem,
$f \left(x\right) = {e}^{x}$ and $g \left(x\right) = 2 x$
By taking the derivative,
$f ' \left(x\right) = {e}^{x}$ and $g ' \left(x\right) = 2$

By Chain Rule,
$y ' = {e}^{2 x} \cdot 2 = 2 {e}^{2 x}$