Theorems · Theorem · real analysis

HasFDerivWithinAt.pow

∀ {𝕜 : Type u_1} {𝔸 : Type u_2} {E : Type u_3} [inst : NontriviallyNormedField 𝕜] [inst_1 : NormedCommRing 𝔸]
  [inst_2 : NormedAddCommGroup E] [inst_3 : NormedAlgebra 𝕜 𝔸] [inst_4 : NormedSpace 𝕜 E] {f : E → 𝔸} {f' : E →L[𝕜] 𝔸}
  {x : E} {s : Set E},
  HasFDerivWithinAt f f' s x → ∀ (n : ℕ), HasFDerivWithinAt (fun x => f x ^ n) ((n • f x ^ (n - 1)) • f') s x

Defined in

Mathlib.Analysis.Calculus.FDeriv.Pow

Cited by

3 results in Mathlib

Foundations

Depth 185 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedCommRingNormedAddCommGroupNormedAlgebraNormedSpace