Theorems · Theorem · real analysis

fderivWithin.snd

∀ {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] {G : Type u_4}
  [inst_5 : NormedAddCommGroup G] [inst_6 : NormedSpace 𝕜 G] {x : E} {s : Set E} {f₂ : E → F × G},
  UniqueDiffWithinAt 𝕜 s x →
    DifferentiableWithinAt 𝕜 f₂ s x →
      fderivWithin 𝕜 (fun x => (f₂ x).2) s x = ContinuousLinearMap.snd 𝕜 F G ∘SL fderivWithin 𝕜 f₂ s x

Defined in

Mathlib.Analysis.Calculus.FDeriv.Prod

Cited by

0 results in Mathlib

Foundations

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

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpace