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partial derivative of a sum

• To: mathgroup at smc.vnet.net
• Subject: [mg59788] partial derivative of a sum
• From: Daniel Roy <droy at mit.edu>
• Date: Sun, 21 Aug 2005 03:51:36 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

I'm wondering if Mathematica can handle expressions such as:

 ClearAll[n, l]
 D[Sum[n[i] l[i], {i, 1, Infinity}], n[10]]

The answer should be l[10], but Mathematica returns 0.
 
 ClearAll[n, l]
 D[Sum[n[i]l[i], {i, 1, 100}], n[10]]

return l[10] as expected.  More generally,

 ClearAll[n, l]
 Assumptions[N \[Element] Integers && N>10, 
             D[Sum[n[i] l[i],{i,1,N}], n[10]]

Thanks, 
Dan Roy

• Follow-Ups:
  • Re: partial derivative of a sum
    • From: Pratik Desai <pdesai1@umbc.edu>