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Following up to EY's comment:
e^x is its own second derivative too. There are two functions that are their own second derivative, and four which are their own fourth derivative.
Cool! So what are the other two (out of three) functions that are their own third derivative? What does their graph look like? And does all this have anything to do with Laplace transforms? Does a sufficiently smooth function have a 1.5th derivative?
Yes, welcome to LW.
I think so.