Theorems · Theorem · real analysis
DifferentiableWithinAt.arsinh
∀ {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] {f : E → ℝ} {s : Set E} {a : E},
DifferentiableWithinAt ℝ f s a → DifferentiableWithinAt ℝ (fun x => Real.arsinh (f x)) s a- Defined in
- Mathlib.Analysis.SpecialFunctions.Arsinh
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 214 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- DifferentiableWithinAtstatement and proof · cited by 453
- Real.arsinhstatement · cited by 55
- DifferentiableAt.comp_differentiableWithinAtproof · cited by 14
- Real.differentiable_arsinhproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- DifferentiableOn.arsinhproof · cited by 0