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Derivatives of functions and equality of those functions

  1. Jun 26, 2012 #1

    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
    \frac{df(x)}{x} = \frac{dg(x)}{dx}
    Does this imply that f(x)=g(x)?

  2. jcsd
  3. Jun 26, 2012 #2


    Staff: Mentor

    Re: Derivatives

    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?
  4. Jun 26, 2012 #3
    Re: Derivatives

    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.
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