Theorems · Theorem · global analysis

fderivWithin_fun_sum

∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type u_2} [inst_1 : NormedAddCommGroup E]
  [inst_2 : NormedSpace 𝕜 E] {F : Type u_3} [inst_3 : NormedAddCommGroup F] [inst_4 : NormedSpace 𝕜 F] {x : E}
  {s : Set E} {ι : Type u_4} {u : Finset ι} {A : ι → E → F},
  UniqueDiffWithinAt 𝕜 s x →
    (∀ i ∈ u, DifferentiableWithinAt 𝕜 (A i) s x) →
      fderivWithin 𝕜 (fun y => ∑ i ∈ u, A i y) s x = ∑ i ∈ u, fderivWithin 𝕜 (A i) s x

Defined in

Mathlib.Analysis.Calculus.FDeriv.Add

Cited by

0 results in Mathlib

Foundations

Depth 170 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpace