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Theorems · Theorem · real analysis

DifferentiableWithinAt.cpow_const

∀ {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℂ E] {f : E → ℂ} {x : E} {s : Set E} {c : ℂ},
  DifferentiableWithinAt ℂ f s x → f x ∈ Complex.slitPlane → DifferentiableWithinAt ℂ (fun x => f x ^ c) s x
Defined in
Mathlib.Analysis.SpecialFunctions.Pow.Deriv
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Foundations
Depth 214 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
NormedAddCommGroupNormedSpace
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Set · cited by 53352SetNormedAddCommGroup · cited by 15752NormedAddCommGroupNormedSpace · cited by 12499NormedSpaceComplex · cited by 5565ComplexDifferentiableWithinAt · cited by 453DifferentiableWithinAtComplex.slitPlane · cited by 113Complex.slitPlanedifferentiableWithinAt_const · cited by 7differentiableWithinAt_co…DifferentiableWithinAt.cpow · cited by 2DifferentiableWithinAt.cp…DifferentiableWithinAt.cpow_c…CITED BYCITES

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