Theorems · Theorem · real analysis

HasDerivWithinAt.comp

∀ {𝕜 : Type u} [inst : NontriviallyNormedField 𝕜] (x : 𝕜) {s : Set 𝕜} {𝕜' : Type u_1}
  [inst_1 : NontriviallyNormedField 𝕜'] [inst_2 : NormedAlgebra 𝕜 𝕜'] {s' : Set 𝕜'} {h : 𝕜 → 𝕜'} {h₂ : 𝕜' → 𝕜'}
  {h' h₂' : 𝕜'},
  HasDerivWithinAt h₂ h₂' s' (h x) →
    HasDerivWithinAt h h' s x → Set.MapsTo h s s' → HasDerivWithinAt (h₂ ∘ h) (h₂' * h') s x

Defined in

Mathlib.Analysis.Calculus.Deriv.Comp

Cited by

4 results in Mathlib

Foundations

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

Assumes

NontriviallyNormedFieldNontriviallyNormedFieldNormedAlgebra