Theorems · Theorem · real analysis
DifferentiableAt.abs_of_neg
∀ {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 x => |f x|) x- Defined in
- Mathlib.Analysis.Calculus.Deriv.Abs
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 174 from the axioms · uses propext, Classical.choice, Quot.sound
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- Realstatement and proof · cited by 25,697
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- absstatement · cited by 1,814
- DifferentiableAtstatement and proof · cited by 617
- DifferentiableAt.compproof · cited by 38
- differentiableAt_abs_negproof · cited by 3
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