Theorems · Theorem · real analysis
HasDerivWithinAt.arctan
∀ {f : ℝ → ℝ} {f' x : ℝ} {s : Set ℝ},
HasDerivWithinAt f f' s x → HasDerivWithinAt (fun x => Real.arctan (f x)) (1 / (1 + f x ^ 2) * f') s x- Cited by
- 1 results in Mathlib
- Foundations
- Depth 208 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- HasDerivWithinAtstatement and proof · cited by 333
- Real.arctanstatement · cited by 111
- HasDerivAt.comp_hasDerivWithinAtproof · cited by 21
- Real.hasDerivAt_arctanproof · cited by 7
Cited by1
Results whose statement or proof uses this declaration.
- derivWithin_arctanproof · cited by 0