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Theorems · Theorem · real analysis

hasFDerivAt_pow

∀ {𝕜 : Type u_1} {𝔸 : Type u_2} [inst : NontriviallyNormedField 𝕜] [inst_1 : NormedCommRing 𝔸]
  [inst_2 : NormedAlgebra 𝕜 𝔸] (n : ℕ) {x : 𝔸},
  HasFDerivAt (fun x => x ^ n) ((n • x ^ (n - 1)) • ContinuousLinearMap.id 𝕜 𝔸) x
Defined in
Mathlib.Analysis.Calculus.FDeriv.Pow
Cited by
0 results in Mathlib
Foundations
Depth 186 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
NontriviallyNormedFieldNormedCommRingNormedAlgebra
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RingHom.id · cited by 18349RingHom.idNontriviallyNormedField · cited by 8742NontriviallyNormedFieldContinuousLinearMap · cited by 5352ContinuousLinearMapNormedAlgebra · cited by 1165NormedAlgebraHasFDerivAt · cited by 350HasFDerivAtContinuousLinearMap.id · cited by 233ContinuousLinearMap.idNormedCommRing · cited by 218NormedCommRinghasFDerivAt_id · cited by 18hasFDerivAt_idHasFDerivAt.pow · cited by 3HasFDerivAt.powhasFDerivAt_powCITED BYCITES

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