Theorems · Theorem · real analysis

fderiv_fun_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} (n : ℕ),
  DifferentiableAt 𝕜 f x → fderiv 𝕜 (fun i => f i ^ n) x = (n • f x ^ (n - 1)) • fderiv 𝕜 f x

Eta-expanded form of fderiv_pow

Defined in

Mathlib.Analysis.Calculus.FDeriv.Pow

Cited by

1 results in Mathlib

Foundations

Depth 187 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedCommRingNormedAddCommGroupNormedAlgebraNormedSpace