Theorems · Theorem · real analysis
HasDerivAt.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')Alias of the forward direction of hasDerivAt_iff_tendsto_slope.
- Defined in
- Mathlib.Analysis.Calculus.Deriv.Slope
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 169 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
- hasDerivAt_iff_tendsto_slopeproof · cited by 9
Cited by1
Results whose statement or proof uses this declaration.
- MonotoneOn.exists_tendsto_deriv_liminf_lintegral_enorm_leproof · cited by 2