Mathlib Map

Theorems · Theorem · real analysis

DifferentiableWithinAt.cpow

∀ {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℂ E] {f g : E → ℂ} {x : E} {s : Set E},
  DifferentiableWithinAt ℂ f s x →
    DifferentiableWithinAt ℂ g s x → f x ∈ Complex.slitPlane → DifferentiableWithinAt ℂ (fun x => f x ^ g x) s x
Defined in
Mathlib.Analysis.SpecialFunctions.Pow.Deriv
Cited by
2 results in Mathlib
Foundations
Depth 213 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
NormedAddCommGroupNormedSpace
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

DifferentiableOn.cpow · cited by 1DifferentiableOn.cpowDifferentiableWithinAt.cpow_const · cited by 0DifferentiableWithinAt.cp…Set · cited by 53352SetNormedAddCommGroup · cited by 15752NormedAddCommGroupNormedSpace · cited by 12499NormedSpaceComplex · cited by 5565ComplexDifferentiableWithinAt · cited by 453DifferentiableWithinAtDifferentiableWithinAt.hasFDerivWithinAt · cited by 132DifferentiableWithinAt.ha…Complex.slitPlane · cited by 113Complex.slitPlaneHasFDerivWithinAt.differentiableWithinAt · cited by 65HasFDerivWithinAt.differe…HasFDerivWithinAt.cpow · cited by 2HasFDerivWithinAt.cpowDifferentiableWithinAt.cpowCITED BYCITES

Cites9

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by2

Results whose statement or proof uses this declaration.