Theorems · Theorem · real analysis
hasStrictDerivAt_zpow
∀ {𝕜 : Type u} [inst : NontriviallyNormedField 𝕜] (m : ℤ) (x : 𝕜),
x ≠ 0 ∨ 0 ≤ m → HasStrictDerivAt (fun x => x ^ m) (↑m * x ^ (m - 1)) x- Defined in
- Mathlib.Analysis.Calculus.Deriv.ZPow
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 188 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- NontriviallyNormedField
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites30
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopologicalSpaceproof · cited by 24,529
- Moduleproof · cited by 20,661
- AddCommGroupproof · cited by 12,871
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- LT.lt.leproof · cited by 2,189
- Nat.cast_zeroproof · cited by 1,870
- mul_assocproof · cited by 1,667
- MulZeroClass.zero_mulproof · cited by 1,625
- ContinuousSMulproof · cited by 1,016
- neg_mulproof · cited by 654
- inv_invproof · cited by 494
- Int.cast_natCastproof · cited by 393
Cited by1
Results whose statement or proof uses this declaration.
- hasDerivAt_zpowproof · cited by 5