Theorems · Theorem · functional analysis
DifferentiableAt.fderiv_norm_self
∀ {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] {x : E},
DifferentiableAt ℝ (fun x => ‖x‖) x → (fderiv ℝ (fun x => ‖x‖) x) x = ‖x‖- Defined in
- Mathlib.Analysis.Calculus.FDeriv.Norm
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 189 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites30
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Realstatement and proof · cited by 25,697
- RingHom.idstatement · cited by 18,349
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- Norm.normstatement and proof · cited by 5,413
- ContinuousLinearMapstatement · cited by 5,352
- mul_oneproof · cited by 3,885
- one_mulproof · cited by 2,841
- add_zeroproof · cited by 2,707
- absproof · cited by 1,814
- one_smulproof · cited by 1,374
Cited by1
Results whose statement or proof uses this declaration.
- norm_fderiv_normproof · cited by 0