Theorems · Theorem · real analysis
DifferentiableOn.hasDerivAt
∀ {𝕜 : Type u} [inst : NontriviallyNormedField 𝕜] {F : Type v} [inst_1 : NormedAddCommGroup F]
[inst_2 : NormedSpace 𝕜 F] {f : 𝕜 → F} {x : 𝕜} {s : Set 𝕜},
DifferentiableOn 𝕜 f s → s ∈ nhds x → HasDerivAt f (deriv f x) x- Defined in
- Mathlib.Analysis.Calculus.Deriv.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 155 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 and proof · 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
- Filterstatement · cited by 8,121
- nhdsstatement and proof · cited by 5,554
- derivstatement · cited by 676
- HasDerivAtstatement · cited by 493
- DifferentiableOnstatement and proof · cited by 419
- HasFDerivAt.hasDerivAtproof · cited by 18
- DifferentiableOn.hasFDerivAtproof · cited by 4
Cited by2
Results whose statement or proof uses this declaration.
- norm_sub_le_integral_of_norm_deriv_le_of_leproof · cited by 1
- taylor_integral_remainderproof · cited by 0