Theorems · Theorem · real analysis

HasStrictFDerivAt.rpow_const

∀ {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] {f : E → ℝ} {f' : StrongDual ℝ E} {x : E}
  {p : ℝ},
  HasStrictFDerivAt f f' x → f x ≠ 0 ∨ 1 ≤ p → HasStrictFDerivAt (fun x => f x ^ p) ((p * f x ^ (p - 1)) • f') x

Defined in

Mathlib.Analysis.SpecialFunctions.Pow.Deriv

Cited by

1 results in Mathlib

Foundations

Depth 214 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpace