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There are several equivalent ways of defining a function. We know that a differentiable function $f : \mathbb{R} \to \mathbb{R}$ is uniquely defined when its values are specified at every point in $\mathbb{R}$. Now the question is : Is the derivative of such a function $f$ always unique ?

PS: Pardon me if its a very trivial question !

EDIT 1: the definition of the derivative is same as usual...i mean that given in the answer by Jonas Meyer and so is the definition of differentiability.

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    @PEV : please let me know what have you edited in the question.2011-01-20
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    at the bottom of the question, there is now a box showing that PEV edited the the question some time ago. You can click on the time there (now it reads 3 mins ago, so just click on the words "3 mins"). This will lead you to the revision history page, which shows that PEV removed the emphasis you placed on the last sentence of the first paragraph.2011-01-20
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    @Willie Wong : that was a subtle edit.Thanks for pointing out. I couldn't notice it the first time i saw before asking.2011-01-20
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    in view of the answer given by PEV below, perhaps you need to clarify whether you are asking for two functions $f,g$ such that their derivatives coincide, or for a function $f$ such that it has "two distinct derivatives". In the latter case you should also update the question with your definition of "differentiable function" and "derivative".2011-01-20
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    @Willie Wong : Ok. give me a minute.thanks2011-01-20

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