Theorems · Theorem · real analysis

DifferentiableAt.div_const

∀ {𝕜 : Type u} [inst : NontriviallyNormedField 𝕜] {x : 𝕜} {𝕜' : Type u_2} [inst_1 : NormedDivisionRing 𝕜']
  [inst_2 : NormedAlgebra 𝕜 𝕜'] {c : 𝕜 → 𝕜'},
  DifferentiableAt 𝕜 c x → ∀ (d : 𝕜'), DifferentiableAt 𝕜 (fun x => c x / d) x

Defined in

Mathlib.Analysis.Calculus.Deriv.Mul

Cited by

9 results in Mathlib

Foundations

Depth 187 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedDivisionRingNormedAlgebra