Theorems · Theorem · real analysis

HasDerivAtFilter.fun_sum

∀ {𝕜 : Type u} [inst : NontriviallyNormedField 𝕜] {F : Type v} [inst_1 : NormedAddCommGroup F]
  [inst_2 : NormedSpace 𝕜 F] {L : Filter (𝕜 × 𝕜)} {ι : Type u_1} {u : Finset ι} {A : ι → 𝕜 → F} {A' : ι → F},
  (∀ i ∈ u, HasDerivAtFilter (A i) (A' i) L) → HasDerivAtFilter (fun y => ∑ i ∈ u, A i y) (∑ i ∈ u, A' i) L

Defined in

Mathlib.Analysis.Calculus.Deriv.Add

Cited by

4 results in Mathlib

Foundations

Depth 166 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpace