Theorems · Theorem · real analysis

DifferentiableWithinAt.zpow

∀ {𝕜 : Type u} [inst : NontriviallyNormedField 𝕜] {E : Type v} [inst_1 : NormedAddCommGroup E]
  [inst_2 : NormedSpace 𝕜 E] {m : ℤ} {f : E → 𝕜} {t : Set E} {a : E},
  DifferentiableWithinAt 𝕜 f t a → f a ≠ 0 ∨ 0 ≤ m → DifferentiableWithinAt 𝕜 (fun x => f x ^ m) t a

Defined in

Mathlib.Analysis.Calculus.Deriv.ZPow

Cited by

1 results in Mathlib

Foundations

Depth 191 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpace