Theorems · Theorem · real analysis
hasDerivAt_iff_tendsto_slope
∀ {𝕜 : Type u} [inst : NontriviallyNormedField 𝕜] {F : Type v} [inst_1 : NormedAddCommGroup F]
[inst_2 : NormedSpace 𝕜 F] {f : 𝕜 → F} {f' : F} {x : 𝕜},
HasDerivAt f f' x ↔ Filter.Tendsto (slope f x) (nhdsWithin x {x}ᶜ) (nhds f')- Defined in
- Mathlib.Analysis.Calculus.Deriv.Slope
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 168 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- nhdsstatement · cited by 5,554
- Filter.Tendstostatement · cited by 3,814
- Compl.complstatement · cited by 2,925
- nhdsWithinstatement · cited by 1,912
- HasDerivAtstatement · cited by 493
- slopestatement · cited by 147
- hasDerivAtFilter_iff_tendsto_slopeproof · cited by 2
Cited by9
Results whose statement or proof uses this declaration.
- expNegInvGlue.hasDerivAt_polynomial_eval_inv_mulproof · cited by 2
- eventually_nhdsWithin_sign_eq_of_deriv_posproof · cited by 2
- Monotone.ae_hasDerivAtproof · cited by 1
- HasDerivAt.tendsto_slopeproof · cited by 1
- ZetaAsymptotics.tendsto_Gamma_term_auxproof · cited by 1
- StieltjesFunction.ae_hasDerivAtproof · cited by 1
- exists_dist_slope_lt_pairwiseDisjoint_hasSumproof · cited by 1
- AnalyticAt.tendsto_mul_logDeriv_simple_zeroproof · cited by 0
- HasDerivAt.continuousAt_divproof · cited by 0