Theorems · Theorem · real analysis

HasDerivWithinAt.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'} {c' d' : 𝕜'},
  HasDerivWithinAt c c' s x →
    HasDerivWithinAt d d' s x → d x ≠ 0 → HasDerivWithinAt (c / d) ((c' * d x - c x * d') / d x ^ 2) s x

Defined in

Mathlib.Analysis.Calculus.Deriv.Inv

Cited by

3 results in Mathlib

Foundations

Depth 186 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNontriviallyNormedFieldNormedAlgebra