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I need a function f:R^2->R continuous in R^2, and such that all its directional derivatives exist, but f must not be differentiable in R^2.

I know examples of functions continuous but not diff., and with all directional derivatives but not diff. But I cant find an example which satisfy all those conditions at the same time.

Thanks in advance.

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    $\begingroup$ possible duplicate of math.stackexchange.com/questions/372070/… $\endgroup$ – GA316 Mar 5 '15 at 22:09
  • $\begingroup$ If you put the title of your post in a search engine and clicked a few results, you'd have an answer in less time than it took to type this question. $\endgroup$ – user147263 Mar 5 '15 at 23:17
  • $\begingroup$ Do you want it to be nowhere differentiable, or not differentiable at one point ? $\endgroup$ – Charles Madeline Mar 18 '18 at 19:20

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