Theorems · Theorem · real analysis

fderivWithin_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} {x : E}
  {s : Set E},
  UniqueDiffWithinAt 𝕜 s x →
    ∀ (n : ℕ), DifferentiableWithinAt 𝕜 f s x → fderivWithin 𝕜 (f ^ n) s x = (n • f x ^ (n - 1)) • fderivWithin 𝕜 f s x

Defined in

Mathlib.Analysis.Calculus.FDeriv.Pow

Cited by

1 results in Mathlib

Foundations

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

Assumes

NontriviallyNormedFieldNormedCommRingNormedAddCommGroupNormedAlgebraNormedSpace