Theorems · Theorem · real analysis
HasFDerivAt.csin
∀ {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℂ E] {f : E → ℂ} {f' : StrongDual ℂ E} {x : E},
HasFDerivAt f f' x → HasFDerivAt (fun x => Complex.sin (f x)) (Complex.cos (f x) • f') x- Cited by
- 2 results in Mathlib
- Foundations
- Depth 203 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- RingHom.idstatement · cited by 18,349
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- Complexstatement and proof · cited by 5,565
- StrongDualstatement and proof · cited by 459
- HasFDerivAtstatement and proof · cited by 350
- Complex.cosstatement · cited by 279
- Complex.sinstatement · cited by 258
- HasDerivAt.comp_hasFDerivAtproof · cited by 20
- Complex.hasDerivAt_sinproof · cited by 10
Cited by2
Results whose statement or proof uses this declaration.
- DifferentiableAt.csinproof · cited by 1
- fderiv_csinproof · cited by 0