mdifferentiableOn_const — Mathlib

English

If f and g are differentiable within s, then the map x ↦ (f x, g x) is differentiable within s with derivative df.prod dg.

Русский

Если f и g дифференцируемы внутри s, то x ↦ (f x, g x) дифференцируема внутри s, производная равна df.prod dg.

LaTeX

$$$ mdifferentiableWithinAt I I' f s x df \to mdifferentiableWithinAt I I'' g s x dg \to mdifferentiableWithinAt I (I' .prod I'') (fun y => (f y, g y)) s x (df.prod dg) $$$

Lean4

theorem mdifferentiableOn_const : MDifferentiableOn I I' (fun _ : M => c) s :=
  mdifferentiable_const.mdifferentiableOn

Похожие утверждения