Theorems · Theorem · real analysis

derivWithin_comp_const_add

∀ {𝕜 : Type u_1} {F : Type u_2} [inst : NontriviallyNormedField 𝕜] [inst_1 : NormedAddCommGroup F]
  [inst_2 : NormedSpace 𝕜 F] (f : 𝕜 → F) (a : 𝕜) (s : Set 𝕜) (x : 𝕜),
  derivWithin (fun x => f (a + x)) s x = derivWithin f (a +ᵥ s) (a + x)

Translation in the domain does not change the derivative.

Defined in

Mathlib.Analysis.Calculus.Deriv.Shift

Cited by

1 results in Mathlib

Foundations

Depth 169 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpace