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Theorems · Theorem · real analysis

HasDerivWithinAt.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} {s : Set 𝕜},
  HasDerivWithinAt f f' s x → ∀ (n : ℕ), HasDerivWithinAt (f ^ n) (↑n * f x ^ (n - 1) * f') s x
Defined in
Mathlib.Analysis.Calculus.Deriv.Pow
Cited by
2 results in Mathlib
Foundations
Depth 187 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
NontriviallyNormedFieldNormedCommRingNormedAlgebra
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Around this declaration

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derivWithin_pow · cited by 1derivWithin_powhasDerivWithinAt_pow · cited by 0hasDerivWithinAt_powSet · cited by 53352SetNontriviallyNormedField · cited by 8742NontriviallyNormedFieldNormedAlgebra · cited by 1165NormedAlgebraHasDerivWithinAt · cited by 333HasDerivWithinAtNormedCommRing · cited by 218NormedCommRingHasDerivWithinAt.fun_pow · cited by 1HasDerivWithinAt.fun_powHasDerivWithinAt.powCITED BYCITES

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Cited by2

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