Theorems · Theorem · real analysis

HasStrictDerivAt.scomp_of_eq

∀ {𝕜 : Type u} [inst : NontriviallyNormedField 𝕜] {F : Type v} [inst_1 : NormedAddCommGroup F]
  [inst_2 : NormedSpace 𝕜 F] (x : 𝕜) {𝕜' : Type u_1} [inst_3 : NontriviallyNormedField 𝕜'] [inst_4 : NormedAlgebra 𝕜 𝕜']
  [inst_5 : NormedSpace 𝕜' F] [IsScalarTower 𝕜 𝕜' F] {h : 𝕜 → 𝕜'} {h' : 𝕜'} {g₁ : 𝕜' → F} {g₁' : F} {y : 𝕜'},
  HasStrictDerivAt g₁ g₁' y → HasStrictDerivAt h h' x → y = h x → HasStrictDerivAt (g₁ ∘ h) (h' • g₁') x

Defined in

Mathlib.Analysis.Calculus.Deriv.Comp

Cited by

0 results in Mathlib

Foundations

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

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNontriviallyNormedFieldNormedAlgebraNormedSpaceIsScalarTower