Can a Function Equal Its Own Derivative?

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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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Axecutioner said:
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).
 
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Oh, didn't think about that. XD I kept trying Trig to make it work...

Are there any other ways?
 
Axecutioner said:
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.
 
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...
 

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