Is it possible...

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

rock.freak667

Sure, if f(x)=e^x, then f'(x) = e^x = f(x).

Axecutioner

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

Are there any other ways?

rock.freak667

if you solve the differential equation

f'(x)=f(x)

You'd see that any multiply of e^x would satisfy the condition. I think that is the only function, that I know of anyhow.

micromass

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...