Theorems · Theorem · real analysis
hasDerivAt_iff_hasFDerivAt
∀ {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' : F},
HasDerivAt f f' x ↔ HasFDerivAt f (ContinuousLinearMap.toSpanSingleton 𝕜 f') xExpressing HasDerivAt f f' x in terms of HasFDerivAt
- Defined in
- Mathlib.Analysis.Calculus.Deriv.Basic
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 106 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopologicalSpacestatement and proof · cited by 24,529
- Modulestatement and proof · cited by 20,661
- AddCommGroupstatement and proof · cited by 12,871
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- ContinuousSMulstatement and proof · cited by 1,016
- HasDerivAtstatement · cited by 493
- HasFDerivAtstatement · cited by 350
- ContinuousLinearMap.toSpanSingletonstatement · cited by 133
Cited by7
Results whose statement or proof uses this declaration.
- HasDerivAt.hasFDerivAtproof · cited by 27
- IsLocalMin.hasDerivAt_eq_zeroproof · cited by 4
- HasDerivAt.star_conjproof · cited by 3
- HasDerivAt.comp_semilinearproof · cited by 2
- IsMIntegralCurveAt.eventually_hasDerivAtproof · cited by 1
- complexOfReal_hasDerivAtproof · cited by 1
- ProbabilityTheory.differentiableOn_complexMGFproof · cited by 1