logDeriv_cosh — Mathlib

English

The logarithmic derivative of the complex hyperbolic cosine is the hyperbolic tangent: logDeriv(Complex.cosh) = Complex.tanh.

Русский

Логарифмическая производная гиперболического косinesa комплексного равна гиперболическому тангенсу: logDeriv(Complex.cosh) = Complex.tanh.

LaTeX

$$$\logDeriv(\mathrm{Complex}.\cosh) = \mathrm{Complex}.\tanh$$$

Lean4

@[simp]
theorem logDeriv_cosh : logDeriv (Complex.cosh) = Complex.tanh :=
  by
  ext
  rw [logDeriv, Complex.deriv_cosh, Pi.div_apply, Complex.tanh]

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