Theorems · Theorem · real analysis
hasStrictDerivAt_inv
∀ {𝕜 : Type u} [inst : NontriviallyNormedField 𝕜] {x : 𝕜}, x ≠ 0 → HasStrictDerivAt Inv.inv (-(x ^ 2)⁻¹) x- Defined in
- Mathlib.Analysis.Calculus.Deriv.Inv
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 166 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- NontriviallyNormedField
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites31
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- Set.ofPredproof · cited by 6,101
- nhdsproof · cited by 5,554
- mul_oneproof · cited by 3,885
- Filter.Tendstoproof · cited by 3,814
- one_mulproof · cited by 2,841
- SProd.sprodproof · cited by 1,750
- sub_selfproof · cited by 996
- one_ne_zeroproof · cited by 885
- Filter.Eventually.monoproof · cited by 646
- div_oneproof · cited by 629
- mul_negproof · cited by 590
Cited by4
Results whose statement or proof uses this declaration.
- hasDerivAt_invproof · cited by 9
- HasStrictDerivAt.fun_divproof · cited by 1
- hasStrictDerivAt_zpowproof · cited by 1
- hasStrictFDerivAt_invproof · cited by 0