Theorems · Theorem · real analysis
DifferentiableOn.arsinh
∀ {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] {f : E → ℝ} {s : Set E},
DifferentiableOn ℝ f s → DifferentiableOn ℝ (fun x => Real.arsinh (f x)) s- Defined in
- Mathlib.Analysis.SpecialFunctions.Arsinh
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 215 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites7
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
- DifferentiableOnstatement and proof · cited by 419
- Real.arsinhstatement · cited by 55
- DifferentiableWithinAt.arsinhproof · cited by 1
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