Theorems · Theorem · real analysis

fderivWithin_comp_derivWithin

∀ {𝕜 : Type u} [inst : NontriviallyNormedField 𝕜] {F : Type v} [inst_1 : NormedAddCommGroup F]
  [inst_2 : NormedSpace 𝕜 F] {E : Type w} [inst_3 : NormedAddCommGroup E] [inst_4 : NormedSpace 𝕜 E] {f : 𝕜 → F} (x : 𝕜)
  {s : Set 𝕜} {l : F → E} {t : Set F},
  DifferentiableWithinAt 𝕜 l t (f x) →
    DifferentiableWithinAt 𝕜 f s x →
      Set.MapsTo f s t → derivWithin (l ∘ f) s x = (fderivWithin 𝕜 l t (f x)) (derivWithin f s x)

Defined in

Mathlib.Analysis.Calculus.Deriv.Comp

Cited by

1 results in Mathlib

Foundations

Depth 172 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpace