Theorems · Theorem · real analysis

HasDerivAt.scomp

∀ {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},
  HasDerivAt g₁ g₁' (h x) → HasDerivAt h h' x → HasDerivAt (g₁ ∘ h) (h' • g₁') x

The chain rule.

Defined in

Mathlib.Analysis.Calculus.Deriv.Comp

Cited by

11 results in Mathlib

Foundations

Depth 169 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNontriviallyNormedFieldNormedAlgebraNormedSpaceIsScalarTower