fun_pow — Mathlib

English

The Fréchet derivative of the coordinate projection map Pi.single i at y is the i-th projection; i.e., fderiv Pi.single i y = π_i.

Русский

Фрете производная отображения Pi.single i по точке y равна i-й проекции; fderiv Pi.single i y = π_i.

LaTeX

$$$\\mathrm{fderiv}(\\Pi\\text{.single } i) = \\pi_i$$$

Lean4

@[fun_prop]
theorem fun_pow (hf : DifferentiableWithinAt 𝕜 f s x) (n : ℕ) : DifferentiableWithinAt 𝕜 (fun x => f x ^ n) s x :=
  let ⟨_, hf'⟩ := hf;
  ⟨_, hf'.pow' n⟩

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