Theorems · Theorem · real analysis

HasDerivAt.conj_conj

∀ {𝕜 : Type u} [inst : NontriviallyNormedField 𝕜] [inst_1 : StarRing 𝕜] {x : 𝕜} [NormedStarGroup 𝕜] {f : 𝕜 → 𝕜}
  {f' : 𝕜},
  HasDerivAt f f' x → HasDerivAt (⇑(starRingEnd 𝕜) ∘ f ∘ ⇑(starRingEnd 𝕜)) ((starRingEnd 𝕜) f') ((starRingEnd 𝕜) x)

If f has derivative f' at z, then conj ∘ f ∘ conj has derivative conj f' at conj z.

Defined in

Mathlib.Analysis.Calculus.Deriv.Star

Cited by

0 results in Mathlib

Foundations

Depth 171 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldStarRingNormedStarGroup