∀ {E : Type u_1} {ι : Type u_2} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℂ E] {U : Set ℂ} {z : ℂ}
  {F : ι → ℂ → E} [CompleteSpace E] {u : ι → ℝ},
  Summable u →
    (∀ (i : ι), DifferentiableOn ℂ (F i) U) →
      IsOpen U →
        (∀ (i : ι), ∀ w ∈ U, ‖F i w‖ ≤ u i) →
          z ∈ U → HasSum (fun i => deriv (F i) z) (deriv (fun w => ∑' (i : ι), F i w) z)