# Repeating/“Periodic” Derivatives? [duplicate]

We know that $Ce^x$ and $0$ are the two functions whose first derivative is equal to itself, but what about derivatives of a higher order? For example, the second derivative of $e^{-x}$ is equal to itself, but not the first, and the fourth derivative of $sin(x)$ is equal to itself.

In short, are there other examples of functions whose nth derivative is equal to itself, where $n>1$?

Thank you kindly!

## marked as duplicate by J. M. is a poor mathematician, Community♦Jun 15 '16 at 1:07

The second derivative of $ce^x+ke^{-x}$ is the same as the original function, same goes for $\cosh(x)$ and $\sinh(x)$.
The third derivative of $e^{\omega x}$ is the same as the original function.