Theorems · Theorem · real analysis

hasFDerivAt_iff_hasDerivAt

∀ {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} {x : 𝕜} [inst_4 : ContinuousSMul 𝕜 F] {f' : 𝕜 →L[𝕜] F},
  HasFDerivAt f f' x ↔ HasDerivAt f (f' 1) x

Expressing HasFDerivAt f f' x in terms of HasDerivAt

Defined in

Mathlib.Analysis.Calculus.Deriv.Basic

Cited by

3 results in Mathlib

Foundations

Depth 106 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldAddCommGroupModuleTopologicalSpaceContinuousSMul