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Re: partial derivative of a sum

• To: mathgroup at smc.vnet.net
• Subject: [mg59806] Re: [mg59788] partial derivative of a sum
• From: Pratik Desai <pdesai1 at umbc.edu>
• Date: Mon, 22 Aug 2005 02:48:23 -0400 (EDT)
• References: <200508210751.DAA26559@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

Daniel Roy wrote:

>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
>
>  
>


Here is my attempt using Subscript and Total

ClearAll[n, l, i, m]
m = 100000
n[i_] = Table[Subscript[n, i], {i, 1, m, 1}];
l[i_] = Table[Subscript[l, i], {i, 1, m, 1}];
D[n[i]*l[i] // Total, Subscript[n, 10]]

Hope this helps

Pratik

-- 
Pratik Desai
Graduate Student
UMBC
Department of Mechanical Engineering
Phone: 410 455 8134

• References:
  • partial derivative of a sum
    • From: Daniel Roy <droy@mit.edu>