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Theorems · Theorem · real analysis

HasDerivAt.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} {f' : 𝔸} {x : 𝕜},
  HasDerivAt f f' x → ∀ (n : ℕ), HasDerivAt (fun i => f i ^ n) (↑n * f x ^ (n - 1) * f') x

Eta-expanded form of HasDerivAt.pow

Defined in
Mathlib.Analysis.Calculus.Deriv.Pow
Cited by
1 results in Mathlib
Foundations
Depth 187 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
NontriviallyNormedFieldNormedCommRingNormedAlgebra
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

iteratedDeriv_mul_pow_sub_of_analytic · cited by 0iteratedDeriv_mul_pow_sub…NontriviallyNormedField · cited by 8742NontriviallyNormedFieldNormedAlgebra · cited by 1165NormedAlgebraHasDerivAt · cited by 493HasDerivAtNormedCommRing · cited by 218NormedCommRingHasDerivAt.pow · cited by 8HasDerivAt.powHasDerivAt.fun_powCITED BYCITES

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Cited by1

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