# Is it possible...

by Axecutioner
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 P: 32 Is it possible for f(x) to be equal to f '(x)? I've been trying all day to make it work and have gotten nothing. Thanks
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P: 6,202
 Quote by Axecutioner Is it possible for f(x) to be equal to f '(x)? I've been trying all day to make it work and have gotten nothing. Thanks
Sure, if f(x)=ex, then f'(x) = ex = f(x).
 P: 32 Oh, didn't think about that. XD I kept trying Trig to make it work.... Are there any other ways?
HW Helper
P: 6,202
Is it possible...

 Quote by Axecutioner Oh, didn't think about that. XD I kept trying Trig to make it work.... Are there any other ways?
if you solve the differential equation

f'(x)=f(x)

You'd see that any multiply of ex would satisfy the condition. I think that is the only function, that I know of anyhow.
 Mentor P: 18,213 Indeed, every function of the form $$f(x)=Ce^x$$, with $$C\in \mathbb{R}$$ will do. There are no other functions that equal it's own derivative...