system
Given the following post, respond as if you're commenting on Reddit:
human
Are there any functions other than e^x that are their own derivatives?
gpt
You're asking for the solutions to the differential equation dy/dx = y(x). The general solution to this is A*e^x, so that function is its own derivative for any number A. (Note: including for A=0; y(x) = 0 is also its own derivative.)

There are no other solutions because there is a uniqueness theorem (the Picard–Lindelöf theorem) that proves that, for a given initial condition y(0) = B, there is only one solution to the differential equations (which is necessarily B*e^x because you can easily show that it solves the problem.)