# What is the 100th derivative of 2e^x?

Dec 6, 2016

Well, you should memorize that the derivative of ${e}^{x}$ is ${e}^{x}$. Therefore, $\frac{{d}^{n}}{{\mathrm{dx}}^{n}} \left[{e}^{x}\right] = {f}^{\left(n\right)} \left(x\right) = {e}^{x}$.

The constant floats out front, so

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

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

$= 2 {e}^{x}$

Since we just proved it in general, what does that tell you about the $100$th derivative?