I searched already a lot about indexed Variables, and it tends to be the most applicable way to use tensor notation. But I am having a hard time to solve for undefined indexed variables:

Here my stylized problem:

F := Table[f[i], {i, 1, n}];

The Derivative gives the correct answer if applied for a specified i=1

D[Sum[f[i], {i, 1, 100}], f[1]]

=1

If I want to solve more generally let say $ i \in [1, 100] $

D[Sum[f[i], {i, 1, 100}], f[i]]

=0

Obviously does not work, how can I solve such a problem generally?