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Theorems · Theorem · real analysis

DifferentiableWithinAt.div_const

∀ {𝕜 : Type u} [inst : NontriviallyNormedField 𝕜] {x : 𝕜} {s : Set 𝕜} {𝕜' : Type u_2} [inst_1 : NormedDivisionRing 𝕜']
  [inst_2 : NormedAlgebra 𝕜 𝕜'] {c : 𝕜 → 𝕜'},
  DifferentiableWithinAt 𝕜 c s x → ∀ (d : 𝕜'), DifferentiableWithinAt 𝕜 (fun x => c x / d) s x
Defined in
Mathlib.Analysis.Calculus.Deriv.Mul
Cited by
1 results in Mathlib
Foundations
Depth 186 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
NontriviallyNormedFieldNormedDivisionRingNormedAlgebra
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Around this declaration

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DifferentiableOn.div_const · cited by 1DifferentiableOn.div_constSet · cited by 53352SetNontriviallyNormedField · cited by 8742NontriviallyNormedFieldNormedAlgebra · cited by 1165NormedAlgebraDifferentiableWithinAt · cited by 453DifferentiableWithinAtNormedDivisionRing · cited by 360NormedDivisionRingDifferentiableWithinAt.hasDerivWithinAt · cited by 85DifferentiableWithinAt.ha…HasDerivWithinAt.differentiableWithinAt · cited by 19HasDerivWithinAt.differen…HasDerivWithinAt.div_const · cited by 1HasDerivWithinAt.div_constDifferentiableWithinAt.div_co…CITED BYCITES

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Cited by1

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