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Differentiation w.r.t. elements of lists

• To: mathgroup at smc.vnet.net
• Subject: [mg79642] Differentiation w.r.t. elements of lists
• From: Daniel Hornung <ds.mpg.de.thispartismydomain.daniel.hornung at insertdomainhere.com>
• Date: Wed, 1 Aug 2007 04:54:54 -0400 (EDT)
• Organization: GWDG, Goettingen
• Reply-to: ds.mpg.de.thispartismydomain.daniel.hornung at insertdomainhere.com

Hello,
I don't know if what I want to do is impossible to do neatly (probably not)
or whether I simply chose the wrong way (maybe).

Basically I want to do componentwise differentiation.  Here's a short test
case:
----
In[1] := h[x_]:=Sum[x[[j]]^2,{j,1,Length[x]}]

In[2] := dh[x_,i_]=D[h[x],x[[i]]]
>From In[2]:=
Part::pspec: Part specification i is neither an integer nor a list of 
integers. Mehr...
Out[2]= 0

In[3]:= Assuming[i\[Element]Integers&&i>0&&i<=n,dh[x_,i_]=D[h[x],x[[i]]]]
>From In[3]:=
Part::pspec: Part specification i is neither an integer nor a list of 
integers. Mehr...
Out[3]= 0
----

What I would want is a result like dh[x_,i_]=2x[[i]], of course.

Another, even shorter test case would be 

D[x[[i]], x[[j]]]

which "should", IMHO, return KroneckerDelta[i,j].

Any ideas or hints how to solve these problems in a nice way?

Thank you in advance,
Daniel Hornung

• Follow-Ups:
  • Re: Differentiation w.r.t. elements of lists
    • From: Carl Woll <carlw@wolfram.com>