Theorems · Theorem · real analysis
hasDerivAt_abs
∀ {x : ℝ}, x ≠ 0 → HasDerivAt (fun x => |x|) (↑(SignType.sign x)) x- Defined in
- Mathlib.Analysis.Calculus.Deriv.Abs
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 173 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Realstatement and proof · cited by 25,697
- absstatement · cited by 1,814
- OrderHomstatement · cited by 934
- HasDerivAtstatement · cited by 493
- SignTypestatement · cited by 318
- SignType.signstatement · cited by 128
- SignType.caststatement · cited by 76
- HasStrictDerivAt.hasDerivAtproof · cited by 52
- hasStrictDerivAt_absproof · cited by 2
Cited by5
Results whose statement or proof uses this declaration.
- differentiableAt_absproof · cited by 4
- deriv_absproof · cited by 1
- hasDerivWithinAt_absproof · cited by 0
- HasFDerivAt.absproof · cited by 0
- HasFDerivWithinAt.absproof · cited by 0