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Theorems · Theorem · real analysis

HasDerivWithinAt.const_cpow

∀ {f : ℂ → ℂ} {s : Set ℂ} {f' x c : ℂ},
  HasDerivWithinAt f f' s x → c ≠ 0 ∨ f x ≠ 0 → HasDerivWithinAt (fun x => c ^ f x) (c ^ f x * Complex.log c * f') s x
Defined in
Mathlib.Analysis.SpecialFunctions.Pow.Deriv
Cited by
1 results in Mathlib
Foundations
Depth 202 from the axioms · uses propext, Classical.choice, Quot.sound
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Around this declaration

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

Complex.derivWithin_const_cpow · cited by 1Complex.derivWithin_const…Set · cited by 53352SetComplex · cited by 5565ComplexHasDerivWithinAt · cited by 333HasDerivWithinAtComplex.log · cited by 187Complex.logHasStrictDerivAt.hasDerivAt · cited by 52HasStrictDerivAt.hasDeriv…HasDerivAt.comp_hasDerivWithinAt · cited by 21HasDerivAt.comp_hasDerivW…Complex.hasStrictDerivAt_const_cpow · cited by 6Complex.hasStrictDerivAt_…HasDerivWithinAt.const_cpowCITED BYCITES

Cites7

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Cited by1

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