Theorems · Theorem · real analysis
derivWithin_inv
∀ {𝕜 : Type u} [inst : NontriviallyNormedField 𝕜] {x : 𝕜} {s : Set 𝕜},
x ≠ 0 → UniqueDiffWithinAt 𝕜 s x → derivWithin (fun x => x⁻¹) s x = -(x ^ 2)⁻¹- Defined in
- Mathlib.Analysis.Calculus.Deriv.Inv
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 182 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- NontriviallyNormedField
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Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- derivWithinstatement · cited by 258
- UniqueDiffWithinAtstatement and proof · cited by 252
- differentiableAt_invproof · cited by 7
- deriv_invproof · cited by 4
- DifferentiableAt.derivWithinproof · cited by 3
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