Theorems · Theorem · real analysis
derivWithin_sqrt
∀ {f : ℝ → ℝ} {s : Set ℝ} {x : ℝ},
DifferentiableWithinAt ℝ f s x →
f x ≠ 0 → UniqueDiffWithinAt ℝ s x → derivWithin (fun x => √(f x)) s x = derivWithin f s x / (2 * √(f x))- Defined in
- Mathlib.Analysis.SpecialFunctions.Sqrt
- 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
- Real.sqrtstatement · cited by 545
- DifferentiableWithinAtstatement and proof · cited by 453
- derivWithinstatement · cited by 258
- UniqueDiffWithinAtstatement and proof · cited by 252
- DifferentiableWithinAt.hasDerivWithinAtproof · cited by 85
- HasDerivWithinAt.derivWithinproof · cited by 62
- HasDerivWithinAt.sqrtproof · cited by 1
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