Theorems · Theorem · real analysis

HasDerivAtFilter.comp_hasFDerivAtFilter

∀ {𝕜 : Type u} [inst : NontriviallyNormedField 𝕜] {E : Type w} [inst_1 : NormedAddCommGroup E]
  [inst_2 : NormedSpace 𝕜 E] {𝕜' : Type u_1} [inst_3 : NontriviallyNormedField 𝕜'] [inst_4 : NormedAlgebra 𝕜 𝕜']
  {h₂ : 𝕜' → 𝕜'} {h₂' : 𝕜'} {L' : Filter (𝕜' × 𝕜')} {f : E → 𝕜'} {f' : E →L[𝕜] 𝕜'} {L'' : Filter (E × E)},
  HasDerivAtFilter h₂ h₂' L' →
    HasFDerivAtFilter f f' L'' → Filter.Tendsto (Prod.map f f) L'' L' → HasFDerivAtFilter (h₂ ∘ f) (h₂' • f') L''

Defined in

Mathlib.Analysis.Calculus.Deriv.Comp

Cited by

6 results in Mathlib

Foundations

Depth 167 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNontriviallyNormedFieldNormedAlgebra