Theorems · Theorem · real analysis

HasStrictDerivAt.fun_div

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

Defined in

Mathlib.Analysis.Calculus.Deriv.Inv

Cited by

1 results in Mathlib

Foundations

Depth 184 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNontriviallyNormedFieldNormedAlgebra