Followup on my previous answer, replying to RJF's comments:
> Your expectation is, I think, wrong....
> do you expect
> diff(sum(y*x[k],k,0,n),x[i]) to also be y?
Yes, if 0<=i<=n. But Maxima currently doesn't ask. At least a noun
form is correct, if not terribly useful.
> how about the specifics
> diff (sum(y*x[k],k,0,5),x[12]) ?
> shouldn't this be 0?
Yes.
> How about
> diff (sum(i^2,i,0,n),i) ? the sum doesn't depend on i. it
> depends on n.
> so the derivative is 0.
Maxima gets this one right; and also diff(...,n) => noun form. A noun
form is reasonable here since the summation is implicitly declaring 'n'
to be an integer. Though I suppose you could also "cheat" and treat the
result of the summation as a continuous function in n and get
(6*n^2+6*n+1)/6.
-s