Theorems · Theorem · real analysis

deriv_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} {x : 𝕜},
  DifferentiableAt 𝕜 f x → ∀ (n : ℕ), deriv (fun i => f i ^ n) x = ↑n * f x ^ (n - 1) * deriv f x

Eta-expanded form of deriv_pow

Defined in

Mathlib.Analysis.Calculus.Deriv.Pow

Cited by

9 results in Mathlib

Foundations

Depth 188 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedCommRingNormedAlgebra