Theorems · Theorem · real analysis
HasFDerivWithinAt.cos
∀ {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] {f : E → ℝ} {f' : StrongDual ℝ E} {x : E}
{s : Set E}, HasFDerivWithinAt f f' s x → HasFDerivWithinAt (fun x => Real.cos (f x)) (-Real.sin (f x) • f') s x- Cited by
- 2 results in Mathlib
- Foundations
- Depth 204 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- Realstatement and proof · cited by 25,697
- RingHom.idstatement · cited by 18,349
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- StrongDualstatement and proof · cited by 459
- Real.cosstatement · cited by 424
- Real.sinstatement · cited by 389
- HasFDerivWithinAtstatement and proof · cited by 356
- HasDerivAt.comp_hasFDerivWithinAtproof · cited by 22
- Real.hasDerivAt_cosproof · cited by 12
Cited by2
Results whose statement or proof uses this declaration.
- DifferentiableWithinAt.cosproof · cited by 1
- fderivWithin_cosproof · cited by 0