Theorems · Theorem · real analysis

HasDerivAt.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} {f' : F} (a x : 𝕜),
  HasDerivAt f f' (a + x) → HasDerivAt (fun x => f (a + x)) f' 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 170 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpace