Differentiate into a sum



On 02/07/07, Stavros Macrakis <macrakis at alum.mit.edu> wrote:
> On 7/1/07, Jordi Gutierrez Hermoso <jordigh at gmail.com> wrote:
> > How can I do something like finding the derivative wrt to x[r] of some
> > function of the sum sum(a[k]*x[k], k, 1, n)?
>
> There is no built-in way.  You could of course write code to do this,
> but it wouldn't be completely trivial... consider cases like
>
>       diff( sum(x[i]*x[n-i], i, 1, n), x[3] )
> or
>       diff( sum( sum( x[i+j], i, 0, j ), j, 0, n) ), x[3] )
>

A CAS should be able to handle both of these cases, no? What other
cases do you think it should be able to do? Maybe I will write some
code to do it.

- Jordi G. H.