Theorems · Theorem · real analysis

derivWithin_comp_mul_left

∀ {𝕜 : Type u_1} {E : Type u_2} [inst : NontriviallyNormedField 𝕜] [inst_1 : NormedAddCommGroup E]
  [inst_2 : NormedSpace 𝕜 E] (c : 𝕜) (f : 𝕜 → E) (s : Set 𝕜) (x : 𝕜),
  derivWithin (fun x => f (c * x)) s x = c • derivWithin f (c • s) (c * x)

Defined in

Mathlib.Analysis.Calculus.Deriv.CompMul

Cited by

2 results in Mathlib

Foundations

Depth 175 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpace