Derivatives of functions and equality of those functions

[Niles]

Hi

I thought of something today coming home from school: If I have two arbitrary real functions f(x) and g(x) and I know that
<br /> \frac{df(x)}{x} = \frac{dg(x)}{dx}<br />
Does this imply that f(x)=g(x)?


Niles.

 

[jedishrfu]

i think you df(x)/dx for the right hand side

no, they might not be the same.

As an example f(x)=x^2 +3 and g(x) = x^2 - 4

What do you get for df(x)/dx and dg(x)/dx?

 

[Niles]

Yes, I meant dx, not x, in the denominator. Thanks for pointing that out.

OK, I see. So it must be correct up to an additive constant. Thanks.