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A function $f$ is defined in $R$, and $f'(0)$ exist.
Let $f(x+y)=f(x)f(y)$ then prove that $f'$ exists for all $x$ in $R$.

I think I have to use two fact:
$f'(0)$ exists
$f(x+y)=f(x)f(y)$
How to combine these two things to prove that statement?

  • 0
    Possible duplicate: http://math.stackexchange.com/questions/64766/solution-for-exponential-functions-functional-equation-by-using-a-definition-of2012-12-16
  • 0
    Related: http://math.stackexchange.com/questions/175607/differentiable-function-not-constant-fxy-fxfy-f0-22012-12-16
  • 0
    Related: http://math.stackexchange.com/questions/151032/if-f-colon-mathbbr-to-mathbbr-is-such-that-f-x-y-f-x-f-y-an2012-12-16

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