Theorems · Theorem · real analysis
HasDerivWithinAt.sqrt
∀ {f : ℝ → ℝ} {s : Set ℝ} {f' x : ℝ},
HasDerivWithinAt f f' s x → f x ≠ 0 → HasDerivWithinAt (fun y => √(f y)) (f' / (2 * √(f x))) s x- Defined in
- Mathlib.Analysis.SpecialFunctions.Sqrt
- 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.
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
- mul_oneproof · cited by 3,885
- Real.sqrtstatement and proof · cited by 545
- HasDerivWithinAtstatement and proof · cited by 333
- div_eq_inv_mulproof · cited by 146
- HasDerivWithinAt.congr_simpproof · cited by 29
- HasDerivAt.comp_hasDerivWithinAtproof · cited by 21
- Real.hasDerivAt_sqrtproof · cited by 6
Cited by1
Results whose statement or proof uses this declaration.
- derivWithin_sqrtproof · cited by 0