differentiable_iteratedDeriv_sin — Mathlib

English

For every n, the n-th derivative of sin is differentiable on the real line.

Русский

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

LaTeX

$$$\\\\forall n \in \u211d, \\\\text{Differentiable}(\\\\mathbb{R}, \\ iteratedDeriv n \\sin)$$$

Lean4

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

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