Theorems · Theorem · real analysis
derivWithin_csin
∀ {f : ℂ → ℂ} {x : ℂ} {s : Set ℂ},
DifferentiableWithinAt ℂ f s x →
UniqueDiffWithinAt ℂ s x → derivWithin (fun x => Complex.sin (f x)) s x = Complex.cos (f x) * derivWithin f s x- Cited by
- 0 results in Mathlib
- Foundations
- Depth 204 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Complexstatement and proof · cited by 5,565
- DifferentiableWithinAtstatement and proof · cited by 453
- Complex.cosstatement · cited by 279
- Complex.sinstatement · cited by 258
- derivWithinstatement · cited by 258
- UniqueDiffWithinAtstatement and proof · cited by 252
- DifferentiableWithinAt.hasDerivWithinAtproof · cited by 85
- HasDerivWithinAt.derivWithinproof · cited by 62
- HasDerivWithinAt.csinproof · cited by 1
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