differentiable_iteratedDeriv_cosh

English

For every n, the n-th derivative of cosh is differentiable on ℝ.

Русский

Для каждого n-ого производного cosh дифференцируема на \u211d.

LaTeX

$$$\\\\forall n \\in \\mathbb{N},\\\\; \\\\text{Differentiable}(\\\\mathbb{R}, \\\\ iteratedDeriv n \\\\cosh)$$$

Lean4

theorem differentiable_iteratedDeriv_cosh (n : ℕ) : Differentiable ℝ (iteratedDeriv n cosh) :=
  match n with
  | 0 => by simp
  | 1 => by simp
  | n + 2 => by simp [differentiable_iteratedDeriv_cosh]

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