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Does there exist a differentiable function $f: \mathbb R \to \mathbb R$ such that its derivative $f'$ is nowhere continuous ?

Souvik Dey
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    take a function that is no-where continuous and take its integral (it is not enough unless some details are taken care of). – Mirko Nov 25 '14 at 04:47
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    @user48481MirkoSwirko: But how do I integrate a nowhere continuous function ? – Souvik Dey Nov 25 '14 at 04:47
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    But if you refer to Riemann Integrable, then nowhere-continuous is not integrable. – Passing By Nov 25 '14 at 04:48
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    This is a pretty deep question and relates to Baire spaces and $G_{\delta}$ sets. See this thread which explains it very, very well: http://math.stackexchange.com/questions/292275/discontinuous-derivative In some sense, this "almost everywhere" behavior is more or less what we naturally think of when we think of "nice" functions so it isn't surprising that it is very difficult to come up with examples where the derivative is nowhere continuous. – Cameron Williams Nov 25 '14 at 04:48

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