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On www.wolframalfa.com Symbolic n-th derivative works.

enter image description here

Edited:

On new version Mathematica 11.1 symbolic n-th derivative works.

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  • $\begingroup$ related: mathematica.stackexchange.com/q/7886/5478 $\endgroup$ – Kuba♦ May 11 '16 at 13:09
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    $\begingroup$ Use SeriesCoefficient[] with an appropriate correction factor instead. $\endgroup$ – J. M.'s ennui♦ May 11 '16 at 14:06
  • $\begingroup$ @J.M. and Seeing your comments you do not know which version of MMA will be.I think that in the next 10.5 or 11. Calculation made by WolframAlfa, are incorrect.Bug in WolframAlfa Engine. :) $\endgroup$ – Mariusz Iwaniuk May 11 '16 at 19:10
  • $\begingroup$ related: (9598) $\endgroup$ – Mr.Wizard May 12 '16 at 12:17
  • $\begingroup$ @Mr.Wizard I think currently the selected duplicate isn't proper, this question is more of a duplicate of the one you linked, and just related to the one selected as the duplicate at the moment. $\endgroup$ – xzczd Mar 10 '17 at 16:05
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You can just write

D[f[x],{x,n}]

To get the n-th derivative for x.

EDIT: Ah sorry now i get what you asked for. You want that Mathematica gives you the sum in your screenshoot.

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    $\begingroup$ You can delete own questions if you want. $\endgroup$ – Kuba♦ May 11 '16 at 13:44

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