My Derivative Is Myself

Calculus Level 1

How many functions are there such that f(x)=f(x)f(x) = f'(x)?

Clarification: While functions such as f(x)=2xf(x)=2^{x} and f(x)=2x+1f(x)=2^{x+1} are in the same family of functions, they are different functions, so if you found those two as the only answers, your answer would be 2.

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