I think you will find that Mathematica provides little support for vectors of "arbitrary length"
and that operators, like taking the derivative, when applied to a sum tend to not operate inside the sum
and that Mathematica will tend to not return results as a sum if there is any way it can evaluate that sum, because Mathematica is what is called "an infinite evaluation system" which means it will perform every evaluation that it can and tend to not leave expressions in unevaluated or partially evaluated form.
So I think I understand what you want to accomplish and I think Mathematica will resist trying to give you your result in the form that you want, with or without other software tools. You can try to to write code and functions to attempt to overcome Mathematica's default behavior, but this is often more challenging than letting Mathematica behave in the default way.