Theorems · Theorem · real analysis
fderiv_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 → fderiv ℝ (fun x => √(f x)) x = (1 / (2 * √(f x))) • fderiv ℝ 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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Cites11
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
- DifferentiableAtstatement and proof · cited by 617
- Real.sqrtstatement · cited by 545
- fderivstatement · cited by 398
- DifferentiableAt.hasFDerivAtproof · cited by 134
- HasFDerivAt.fderivproof · cited by 93
- HasFDerivAt.sqrtproof · cited by 2
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