Theorems · Theorem · real analysis

logDeriv_comp

∀ {𝕜 : Type u_1} {𝕜' : Type u_2} [inst : NontriviallyNormedField 𝕜] [inst_1 : NontriviallyNormedField 𝕜']
  [inst_2 : NormedAlgebra 𝕜 𝕜'] {f : 𝕜' → 𝕜'} {g : 𝕜 → 𝕜'} {x : 𝕜},
  DifferentiableAt 𝕜' f (g x) → DifferentiableAt 𝕜 g x → logDeriv (f ∘ g) x = logDeriv f (g x) * deriv g x

Defined in: Mathlib.Analysis.Calculus.LogDeriv
Cited by: 3 results in Mathlib
Foundations: Depth 173 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: NontriviallyNormedField NontriviallyNormedField NormedAlgebra

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Cites6

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

NontriviallyNormedFieldstatement and proof · cited by 8,742
NormedAlgebrastatement and proof · cited by 1,165
derivstatement and proof · cited by 676
DifferentiableAtstatement and proof · cited by 617
logDerivstatement · cited by 71
deriv_compproof · cited by 8

Cited by3

Results whose statement or proof uses this declaration.

ModularForm.logDeriv_qParamproof · cited by 1
logDeriv_sin_div_eq_cotproof · cited by 1
ModularForm.logDeriv_one_sub_mul_cexp_compproof · cited by 0