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Theorems · Theorem · real analysis

HasStrictDerivAt.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},
  HasStrictDerivAt f f' x → ∀ (n : ℕ), HasStrictDerivAt (f ^ n) (↑n * f x ^ (n - 1) * f') x
Defined in
Mathlib.Analysis.Calculus.Deriv.Pow
Cited by
1 results in Mathlib
Foundations
Depth 186 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
NontriviallyNormedFieldNormedCommRingNormedAlgebra
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Around this declaration

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hasStrictDerivAt_pow · cited by 4hasStrictDerivAt_powNontriviallyNormedField · cited by 8742NontriviallyNormedFieldNormedAlgebra · cited by 1165NormedAlgebraNormedCommRing · cited by 218NormedCommRingHasStrictDerivAt · cited by 163HasStrictDerivAtHasStrictDerivAt.fun_pow · cited by 1HasStrictDerivAt.fun_powHasStrictDerivAt.powCITED BYCITES

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