Can a Function Equal Its Own Derivative?

  • Thread starter Axecutioner
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In summary, it is possible for f(x) to be equal to f '(x) if the function is of the form f(x)=Ce^x, where C is any real number. No other functions are known to satisfy this condition.
  • #1
Axecutioner
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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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  • #2
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).
 
Last edited by a moderator:
  • #3
Oh, didn't think about that. XD I kept trying Trig to make it work...

Are there any other ways?
 
  • #4
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.
 
  • #5
Indeed, every function of the form [tex]f(x)=Ce^x[/tex], with [tex]C\in \mathbb{R}[/tex] will do. There are no other functions that equal it's own derivative...
 

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