Theorems · Theorem · real analysis
HasDerivAt.tendsto_slope_zero_right
∀ {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} [inst_3 : Preorder 𝕜],
HasDerivAt f f' x → Filter.Tendsto (fun t => t⁻¹ • (f (x + t) - f x)) (nhdsWithin 0 (Set.Ioi 0)) (nhds f')- Defined in
- Mathlib.Analysis.Calculus.Deriv.Slope
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 172 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- Preorderstatement and proof · cited by 7,952
- nhdsstatement · cited by 5,554
- Filter.Tendstostatement · cited by 3,814
- nhdsWithinstatement · cited by 1,912
- Set.Ioistatement · cited by 1,463
- HasDerivAtstatement and proof · cited by 493
- Filter.Tendsto.mono_leftproof · cited by 125
- nhdsGT_le_nhdsNEproof · cited by 10
- HasDerivAt.tendsto_slope_zeroproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- Real.not_differentiableAt_rpow_const_zeroproof · cited by 1