I am trying to find the numerical derivative of a function whose argument defines the bounds of a numerical integral.

test[u_?NumericQ] := NIntegrate[x^5, {x, 0, u}]
ND[test[u], u, 2]

When I input this I receive the following error message: "NIntegrate::nlim: x = u is not a valid limit of integration." I figured that the inclusion of ?NumericQ in the function definition would take care of this type of issue. Can someone explain why I am receiving this error message?


closed as off-topic by bbgodfrey, Bob Hanlon, m_goldberg, Michael E2, dr.blochwave Jul 16 '15 at 7:59

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    $\begingroup$ Evaluate ClearAll@test and try again. $\endgroup$ – Karsten 7. Jul 15 '15 at 21:56
  • $\begingroup$ With Mathematica 10.1, I receive no error message, but ND[test[u], u, 2] returns unevaluated. However, if I begin the notebook with the required Needs["NumericalCalculus"], it returns 32`, as it should $\endgroup$ – bbgodfrey Jul 15 '15 at 21:57
  • $\begingroup$ @bbgodfrey OP forgot to mention that one has to load the NumericalCalculus` package to have access to ND. I cannot reproduce the error either on 10.1. I suspect that @Karsten may be right, and it may be a spurious definition problem. $\endgroup$ – MarcoB Jul 15 '15 at 21:59
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    $\begingroup$ @Karsten7 was right. I just had to evaluate ClearAll@test and then it worked fine. Thank you! $\endgroup$ – scottb66 Jul 16 '15 at 15:08