Theorems · Theorem · real analysis
DifferentiableOn.fun_pow
∀ {𝕜 : Type u_1} {𝔸 : Type u_2} {E : Type u_3} [inst : NontriviallyNormedField 𝕜] [inst_1 : NormedRing 𝔸]
[inst_2 : NormedAddCommGroup E] [inst_3 : NormedAlgebra 𝕜 𝔸] [inst_4 : NormedSpace 𝕜 E] {f : E → 𝔸} {s : Set E},
DifferentiableOn 𝕜 f s → ∀ (n : ℕ), DifferentiableOn 𝕜 (fun i => f i ^ n) sEta-expanded form of DifferentiableOn.pow
- Defined in
- Mathlib.Analysis.Calculus.FDeriv.Pow
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 188 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.
- Setstatement · cited by 53,352
- NormedAddCommGroupstatement · cited by 15,752
- NormedSpacestatement · cited by 12,499
- NontriviallyNormedFieldstatement · cited by 8,742
- NormedAlgebrastatement · cited by 1,165
- NormedRingstatement · cited by 924
- DifferentiableOnstatement · cited by 419
- DifferentiableOn.powproof · cited by 2
Cited by7
Results whose statement or proof uses this declaration.
- PeriodPair.eqOn_deriv_weierstrassPExcept_derivWeierstrassPExceptproof · cited by 3
- PeriodPair.differentiableOn_weierstrassPExceptproof · cited by 3
- PeriodPair.differentiableOn_derivWeierstrassPExceptproof · cited by 2
- ModularForm.differentiableOn_tprod_one_sub_powproof · cited by 2
- ModularForm.logDeriv_eta_eq_E2proof · cited by 1
- tendsto_logDeriv_euler_sin_divproof · cited by 1
- ModularForm.differentiableOn_tprod_one_sub_pow_powproof · cited by 1