Theorems · Theorem · real analysis
fderiv_inv
∀ {𝕜 : Type u} [inst : NontriviallyNormedField 𝕜] {x : 𝕜},
fderiv 𝕜 (fun x => x⁻¹) x = ContinuousLinearMap.toSpanSingleton 𝕜 (-(x ^ 2)⁻¹)- Defined in
- Mathlib.Analysis.Calculus.Deriv.Inv
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 173 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.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- RingHom.idstatement and proof · cited by 18,349
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- ContinuousLinearMapstatement and proof · cited by 5,352
- fderivstatement · cited by 398
- ContinuousLinearMap.toSpanSingletonstatement and proof · cited by 133
- toSpanSingleton_derivproof · cited by 4
- deriv_invproof · cited by 4
Cited by1
Results whose statement or proof uses this declaration.
- fderivWithin_invproof · cited by 0