Theorems · Theorem · real analysis
HasFDerivAt.sqrt
∀ {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] {f : E → ℝ} {x : E} {f' : StrongDual ℝ E},
HasFDerivAt f f' x → f x ≠ 0 → HasFDerivAt (fun y => √(f y)) ((1 / (2 * √(f x))) • f') x- Defined in
- Mathlib.Analysis.SpecialFunctions.Sqrt
- Cited by
- 2 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.
- 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
- Real.sqrtstatement · cited by 545
- StrongDualstatement and proof · cited by 459
- HasFDerivAtstatement and proof · cited by 350
- HasDerivAt.comp_hasFDerivAtproof · cited by 20
- Real.hasDerivAt_sqrtproof · cited by 6
Cited by2
Results whose statement or proof uses this declaration.
- DifferentiableAt.sqrtproof · cited by 1
- fderiv_sqrtproof · cited by 0