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taking partial derivatives with respect to vector elements: need help with syntax

• To: mathgroup at smc.vnet.net
• Subject: [mg72859] taking partial derivatives with respect to vector elements: need help with syntax
• From: kai_spam at web.de
• Date: Tue, 23 Jan 2007 04:27:05 -0500 (EST)

Hi, I'd appreciate any help on the following simply(?) syntax problem:

I would like to take a partial derivative with respect to a variable
which is indexed within a sum.
Among other things I'm trying the following:

Sum[x[[i]], {i, N}]

which works when I specify x={1,2,3} and N=3, but I want to keep x and
N unspecified. In which case it produces the message:

Part:::pspec : Part specification i is neither an integer nor a list of
integers.

I am aiming for something similar to the following:

D[Sum[x[[i]],{i,N}],x[2]] or even D[Sum[x[[i]],{i,N}],x[j]]

I realize this is quite a rookie-question but I couldn't figure it out
with the mathematica help + book.
Thanks in advance, Kai