Theorems · Theorem · functional analysis

fderivWithin_comp_smul

∀ {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] {f : E → F}
  {s : Set E} {x : E} (c : 𝕜),
  UniqueDiffWithinAt 𝕜 s x → fderivWithin 𝕜 (fun x => f (c • x)) s x = c • fderivWithin 𝕜 f (c • s) (c • x)

Defined in

Mathlib.Analysis.Calculus.FDeriv.Equiv

Cited by

1 results in Mathlib

Foundations

Depth 175 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpace