Theorems · Theorem · global analysis

fderiv_continuousMultilinear_apply_const

∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type u_2} [inst_1 : NormedAddCommGroup E]
  [inst_2 : NormedSpace 𝕜 E] {x : E} {ι : Type u_5} {M : ι → Type u_6} [inst_3 : (i : ι) → NormedAddCommGroup (M i)]
  [inst_4 : (i : ι) → NormedSpace 𝕜 (M i)] {H : Type u_7} [inst_5 : NormedAddCommGroup H] [inst_6 : NormedSpace 𝕜 H]
  {c : E → ContinuousMultilinearMap 𝕜 M H} [inst_7 : Fintype ι],
  DifferentiableAt 𝕜 c x → ∀ (u : (i : ι) → M i), fderiv 𝕜 (fun y => (c y) u) x = (fderiv 𝕜 c x).flipMultilinear u

Defined in

Mathlib.Analysis.Calculus.FDeriv.CompCLM

Cited by

2 results in Mathlib

Foundations

Depth 177 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpaceFintype