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Theorems · Theorem · real analysis

logDeriv_apply

∀ {𝕜 : Type u_1} {𝕜' : Type u_2} [inst : NontriviallyNormedField 𝕜] [inst_1 : NontriviallyNormedField 𝕜']
  [inst_2 : NormedAlgebra 𝕜 𝕜'] (f : 𝕜 → 𝕜') (x : 𝕜), logDeriv f x = deriv f x / f x
Defined in
Mathlib.Analysis.Calculus.LogDeriv
Cited by
4 results in Mathlib
Foundations
Depth 106 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
NontriviallyNormedFieldNontriviallyNormedFieldNormedAlgebra
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

logDeriv_fun_zpow · cited by 4logDeriv_fun_zpowComplex.digamma_one · cited by 0Complex.digamma_oneComplex.digamma_apply_add_one · cited by 0Complex.digamma_apply_add…Complex.digamma_one_half · cited by 0Complex.digamma_one_halfNontriviallyNormedField · cited by 8742NontriviallyNormedFieldNormedAlgebra · cited by 1165NormedAlgebraderiv · cited by 676derivlogDeriv · cited by 71logDerivlogDeriv_applyCITED BYCITES

Cites4

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Cited by4

Results whose statement or proof uses this declaration.