Derivative of vector given the sum of its n elements?

Questions
1

How can I calculate the differentiation of qi if I have the sum of n qi

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2

Maybe this:

W1 = (\[Alpha] - (Sum[Subscript[q, j], {j, 1, n}]) - Subscript[w, 
      i]) Subscript[q, i] - 
   t Subscript[e, i]  - (\[Gamma]/2) (Subscript[a, i])^2 - K;
Simplify[D[W1, Subscript[q, i]], Element[i, Integers] && 1 <= i <= n]
3

Thank you very much.