Theorems · Theorem · real analysis
derivWithin_arctan
∀ {f : ℝ → ℝ} {x : ℝ} {s : Set ℝ},
DifferentiableWithinAt ℝ f s x →
UniqueDiffWithinAt ℝ s x → derivWithin (fun x => Real.arctan (f x)) s x = 1 / (1 + f x ^ 2) * derivWithin f s x- Cited by
- 0 results in Mathlib
- Foundations
- Depth 209 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites9
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
- DifferentiableWithinAtstatement and proof · cited by 453
- derivWithinstatement · cited by 258
- UniqueDiffWithinAtstatement and proof · cited by 252
- Real.arctanstatement · cited by 111
- DifferentiableWithinAt.hasDerivWithinAtproof · cited by 85
- HasDerivWithinAt.derivWithinproof · cited by 62
- HasDerivWithinAt.arctanproof · cited by 1
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