Theorems · Theorem · real analysis
HasStrictFDerivAt.arctan
∀ {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.arctan (f x)) ((1 / (1 + f x ^ 2)) • f') x- Cited by
- 0 results in Mathlib
- Foundations
- Depth 207 from the axioms · uses propext, Classical.choice, Quot.sound
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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
- ContinuousLinearMapstatement · cited by 5,352
- StrongDualstatement and proof · cited by 459
- HasStrictFDerivAtstatement and proof · cited by 261
- Real.arctanstatement · cited by 111
- HasStrictDerivAt.comp_hasStrictFDerivAtproof · cited by 19
- Real.hasStrictDerivAt_arctanproof · cited by 3
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