Theorems · Theorem · real analysis

iteratedFDeriv_apply_eq_iteratedDeriv_mul_prod

∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {F : Type u_2} [inst_1 : NormedAddCommGroup F]
  [inst_2 : NormedSpace 𝕜 F] {n : ℕ} {f : 𝕜 → F} {x : 𝕜} {m : Fin n → 𝕜},
  (iteratedFDeriv 𝕜 n f x) m = (∏ i, m i) • iteratedDeriv n f x

The n-th Fréchet derivative applied to a vector (m 0, ..., m (n-1)) is the derivative multiplied by the product of the m is.

Defined in

Mathlib.Analysis.Calculus.IteratedDeriv.Defs

Cited by

2 results in Mathlib

Foundations

Depth 177 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpace