Theorems · Theorem · functional analysis

hasFDerivAt_norm_rpow

∀ {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : InnerProductSpace ℝ E] (x : E) {p : ℝ},
  1 < p → HasFDerivAt (fun x => ‖x‖ ^ p) ((p * ‖x‖ ^ (p - 2)) • (innerSL ℝ) x) x

Defined in

Mathlib.Analysis.InnerProductSpace.NormPow

Cited by

5 results in Mathlib

Foundations

Depth 215 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupInnerProductSpace