Theorems · Theorem · real analysis

logDeriv_mul

∀ {𝕜 : Type u_1} {𝕜' : Type u_2} [inst : NontriviallyNormedField 𝕜] [inst_1 : NontriviallyNormedField 𝕜']
  [inst_2 : NormedAlgebra 𝕜 𝕜'] {f g : 𝕜 → 𝕜'} (x : 𝕜),
  f x ≠ 0 →
    g x ≠ 0 →
      DifferentiableAt 𝕜 f x → DifferentiableAt 𝕜 g x → logDeriv (fun z => f z * g z) x = logDeriv f x + logDeriv g x

Defined in

Mathlib.Analysis.Calculus.LogDeriv

Cited by

3 results in Mathlib

Foundations

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

Assumes

NontriviallyNormedFieldNontriviallyNormedFieldNormedAlgebra