Theorems · Theorem · real analysis
hasDerivAt_inv
∀ {𝕜 : Type u} [inst : NontriviallyNormedField 𝕜] {x : 𝕜}, x ≠ 0 → HasDerivAt (fun y => y⁻¹) (-(x ^ 2)⁻¹) x- Defined in
- Mathlib.Analysis.Calculus.Deriv.Inv
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 168 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.
Cites4
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
- HasDerivAtstatement · cited by 493
- HasStrictDerivAt.hasDerivAtproof · cited by 52
- hasStrictDerivAt_invproof · cited by 4
Cited by9
Results whose statement or proof uses this declaration.
- deriv_invproof · cited by 4
- HasDerivAt.lhopital_zero_atTop_on_Ioiproof · cited by 3
- HasDerivWithinAt.invproof · cited by 3
- hasFDerivAt_invproof · cited by 2
- expNegInvGlue.hasDerivAt_polynomial_eval_inv_mulproof · cited by 2
- differentiableAt_inv_iffproof · cited by 1
- HasDerivWithinAt.fun_divproof · cited by 1
- EuclideanGeometry.hasFDerivAt_inversionproof · cited by 0
- hasDerivWithinAt_invproof · cited by 0