Theorems · Theorem · real analysis

HasDerivWithinAt.fun_pow

∀ {𝕜 : Type u_1} {𝔸 : Type u_2} [inst : NontriviallyNormedField 𝕜] [inst_1 : NormedCommRing 𝔸]
  [inst_2 : NormedAlgebra 𝕜 𝔸] {f : 𝕜 → 𝔸} {f' : 𝔸} {x : 𝕜} {s : Set 𝕜},
  HasDerivWithinAt f f' s x → ∀ (n : ℕ), HasDerivWithinAt (fun x => f x ^ n) (↑n * f x ^ (n - 1) * f') s x

Defined in

Mathlib.Analysis.Calculus.Deriv.Pow

Cited by

1 results in Mathlib

Foundations

Depth 186 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedCommRingNormedAlgebra