Theorems · Theorem · real analysis

derivWithin_fun_div

∀ {𝕜 : Type u} [inst : NontriviallyNormedField 𝕜] {x : 𝕜} {s : Set 𝕜} {𝕜' : Type u_1}
  [inst_1 : NontriviallyNormedField 𝕜'] [inst_2 : NormedAlgebra 𝕜 𝕜'] {c d : 𝕜 → 𝕜'},
  DifferentiableWithinAt 𝕜 c s x →
    DifferentiableWithinAt 𝕜 d s x →
      d x ≠ 0 → derivWithin (fun x => c x / d x) s x = (derivWithin c s x * d x - c x * derivWithin d s x) / d x ^ 2

Defined in

Mathlib.Analysis.Calculus.Deriv.Inv

Cited by

1 results in Mathlib

Foundations

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

Assumes

NontriviallyNormedFieldNontriviallyNormedFieldNormedAlgebra