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Theorems · Theorem · real analysis

fderivWithin_inv

∀ {𝕜 : Type u} [inst : NontriviallyNormedField 𝕜] {x : 𝕜} {s : Set 𝕜},
  x ≠ 0 →
    UniqueDiffWithinAt 𝕜 s x → fderivWithin 𝕜 (fun x => x⁻¹) s x = ContinuousLinearMap.toSpanSingleton 𝕜 (-(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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Set · cited by 53352SetRingHom.id · cited by 18349RingHom.idNontriviallyNormedField · cited by 8742NontriviallyNormedFieldContinuousLinearMap · cited by 5352ContinuousLinearMapfderivWithin · cited by 357fderivWithinUniqueDiffWithinAt · cited by 252UniqueDiffWithinAtContinuousLinearMap.toSpanSingleton · cited by 133ContinuousLinearMap.toSpa…DifferentiableAt.fderivWithin · cited by 9DifferentiableAt.fderivWi…differentiableAt_inv · cited by 7differentiableAt_invfderiv_inv · cited by 1fderiv_invfderivWithin_invCITED BYCITES

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