Theorems · Theorem · real analysis
HasStrictFDerivAt.cos
∀ {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] {f : E → ℝ} {f' : StrongDual ℝ E} {x : E},
HasStrictFDerivAt f f' x → HasStrictFDerivAt (fun x => Real.cos (f x)) (-Real.sin (f x) • f') x- Cited by
- 1 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.
- 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
- HasStrictFDerivAtstatement and proof · cited by 261
- HasStrictDerivAt.comp_hasStrictFDerivAtproof · cited by 19
- Real.hasStrictDerivAt_cosproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- Real.hasStrictFDerivAt_rpow_of_negproof · cited by 2