Re: Differentiating sums
- To: mathgroup at smc.vnet.net
- Subject: [mg63815] Re: [mg63770] Differentiating sums
- From: Bob Hanlon <hanlonr at cox.net>
- Date: Sun, 15 Jan 2006 05:43:28 -0500 (EST)
- Reply-to: hanlonr at cox.net
- Sender: owner-wri-mathgroup at wolfram.com
Clear[x];
x/:D[Sum[expr_,{i_Symbol,imin_:1,imax_}],x[k_]]:=
D[expr/.{i:>k},x[k]];
prod=Sum[x[i] y[i],{i,n}];
D[prod,x[j]]
y[j]
Bob Hanlon
>
> From: "Zvi Tarem" <zvi.tarem at cern.ch>
To: mathgroup at smc.vnet.net
> Subject: [mg63815] [mg63770] Differentiating sums
>
> How can I use Mathematica to represent sums in a way that can be
> differentiated correctly? Here is a trivial example:
>
> If x and y are both vectors of length N then the derivative of the product
> of the vectors with respect to any element x[i] is simply y[i]. I cannot
> make Mathematica 'understand' the concept of indexing. Here is what I
tried:
>
> prod = Sum[x[i] y[i], {i, N}]
> D[prod, x[j]]
> I get 0
>
> D[prod, x[i]]
> I get Sum[y[i],{i,N}] which is wrong.
>
> The same for subscript notation.
>
> Then I tried Array[] and Part[], but they require constants as the limit and
> selectors.
>
> Can anyone help?
>
>
>