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Theorems · Theorem · real analysis

DifferentiableAt.csin

∀ {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℂ E] {f : E → ℂ} {x : E},
  DifferentiableAt ℂ f x → DifferentiableAt ℂ (fun x => Complex.sin (f x)) x
Defined in
Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv
Cited by
1 results in Mathlib
Foundations
Depth 204 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
NormedAddCommGroupNormedSpace
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Around this declaration

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

Differentiable.csin · cited by 0Differentiable.csinNormedAddCommGroup · cited by 15752NormedAddCommGroupNormedSpace · cited by 12499NormedSpaceComplex · cited by 5565ComplexDifferentiableAt · cited by 617DifferentiableAtComplex.sin · cited by 258Complex.sinDifferentiableAt.hasFDerivAt · cited by 134DifferentiableAt.hasFDeri…HasFDerivAt.differentiableAt · cited by 83HasFDerivAt.differentiabl…HasFDerivAt.csin · cited by 2HasFDerivAt.csinDifferentiableAt.csinCITED BYCITES

Cites8

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Cited by1

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