Theorems · Theorem · real analysis
DifferentiableAt.sqrt
∀ {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] {f : E → ℝ} {x : E},
DifferentiableAt ℝ f x → f x ≠ 0 → DifferentiableAt ℝ (fun y => √(f y)) x- Defined in
- Mathlib.Analysis.SpecialFunctions.Sqrt
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 209 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- DifferentiableAtstatement and proof · cited by 617
- Real.sqrtstatement · cited by 545
- DifferentiableAt.hasFDerivAtproof · cited by 134
- HasFDerivAt.differentiableAtproof · cited by 83
- HasFDerivAt.sqrtproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- Differentiable.sqrtproof · cited by 0