Theorems · Theorem · real analysis

hasFDerivAtFilter_iff_hasDerivAtFilter

∀ {𝕜 : Type u} [inst : NontriviallyNormedField 𝕜] {F : Type v} [inst_1 : AddCommGroup F] [inst_2 : Module 𝕜 F]
  [inst_3 : TopologicalSpace F] {f : 𝕜 → F} {L : Filter (𝕜 × 𝕜)} [inst_4 : ContinuousSMul 𝕜 F] {f' : 𝕜 →L[𝕜] F},
  HasFDerivAtFilter f f' L ↔ HasDerivAtFilter f (f' 1) L

Expressing HasFDerivAtFilter f f' x L in terms of HasDerivAtFilter

Defined in

Mathlib.Analysis.Calculus.Deriv.Basic

Cited by

4 results in Mathlib

Foundations

Depth 105 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldAddCommGroupModuleTopologicalSpaceContinuousSMul