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I am looking to take the derivative of $\partial _n(\sum_ {j=n/2}^{n} f(n,j))$ and I am not sure how to go about doing it. Can Anyone point Me in the direction of information about how to proceed? Thanks. [Note: While I did see the answer at What is the derivative of a summation with respect to it's upper limit?, I get the impression from the comments the answers given are wrong.]

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  • As written, your function is defined only for integers $n$ (perhaps even only for even integers); in that context, derivatives make no sense. If you have in mind a function that is defined for all real numbers $n$, you should be specific about what you mean. – Greg Martin Mar 20 '13 at 02:55
  • @GregMartin: I'm not sure that's necessarily true. Consider the function $f(n,j) = nj$. The derivative of that function with respect to n is $f' = j$. – xuinkrbin. Mar 20 '13 at 03:38
  • True but irrelevant. What, for example, do you mean by $\sum_{j=\pi/2}^\pi f(\pi,j)$? – Greg Martin Mar 20 '13 at 06:25
  • You can find your answer Here: http://math.stackexchange.com/questions/248203/what-is-the-derivative-of-a-summation-with-respect-to-its-upper-limit –  Oct 08 '13 at 14:40

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