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I know that there are functions which are continuous but not differentiable, but are there functions which are not continuous, but differentiable?

JohnnyTheJet
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  • See http://www-math.mit.edu/~djk/18_01/chapter02/proof04.html and http://math.stackexchange.com/questions/269666/how-to-prove-differentiability-implies-continuity-with-epsilon-delta-definit – lab bhattacharjee Dec 15 '14 at 05:43
  • @ml0105 The OP is asking the opposite question to that one. –  Dec 15 '14 at 05:45

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The differrentiablility is stronger than continuity hence the answer is: no. However your question is not naive: function can have partial derivatives but be noncontinuous in a chosen point.

Przemysław Scherwentke
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