Theorems · Theorem · real analysis

HasDerivAtFilter.comp

∀ {𝕜 : Type u} [inst : NontriviallyNormedField 𝕜] {L : Filter (𝕜 × 𝕜)} {𝕜' : Type u_1}
  [inst_1 : NontriviallyNormedField 𝕜'] [inst_2 : NormedAlgebra 𝕜 𝕜'] {h : 𝕜 → 𝕜'} {h₂ : 𝕜' → 𝕜'} {h' h₂' : 𝕜'}
  {L' : Filter (𝕜' × 𝕜')},
  HasDerivAtFilter h₂ h₂' L' →
    HasDerivAtFilter h h' L → Filter.Tendsto (Prod.map h h) L L' → HasDerivAtFilter (h₂ ∘ h) (h₂' * h') L

Defined in

Mathlib.Analysis.Calculus.Deriv.Comp

Cited by

3 results in Mathlib

Foundations

Depth 168 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNontriviallyNormedFieldNormedAlgebra