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

Aug 21, 2016

You're going to hate me, but you have the derivative already.

The derivative of ${e}^{x}$ is itself, and constants can be floated out of the derivative. So, what you have is:

$\textcolor{b l u e}{\frac{d}{\mathrm{dx}} \left[2 {e}^{x}\right]}$

$= 2 \frac{d}{\mathrm{dx}} \left[{e}^{x}\right]$

$= \textcolor{b l u e}{2 {e}^{x}}$

You don't do anything with the chain rule, because $\frac{d}{\mathrm{dx}} \left[{e}^{u}\right] = {e}^{u} \left(\frac{\mathrm{du}}{\mathrm{dx}}\right)$, but since $u \left(x\right) = x$, $\frac{\mathrm{du}}{\mathrm{dx}} = 1$, and therefore, $\frac{d}{\mathrm{dx}} \left[{e}^{x}\right] = {e}^{x} \cdot 1 = {e}^{x}$.