Theorems · Theorem · real analysis
DifferentiableAt.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} {x : E},
DifferentiableAt 𝕜 f x → ∀ (n : ℕ), DifferentiableAt 𝕜 (fun i => f i ^ n) xEta-expanded form of DifferentiableAt.pow
- Defined in
- Mathlib.Analysis.Calculus.FDeriv.Pow
- Cited by
- 8 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.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- NormedAddCommGroupstatement · cited by 15,752
- NormedSpacestatement · cited by 12,499
- NontriviallyNormedFieldstatement · cited by 8,742
- NormedAlgebrastatement · cited by 1,165
- NormedRingstatement · cited by 924
- DifferentiableAtstatement · cited by 617
- DifferentiableAt.powproof · cited by 3
Cited by8
Results whose statement or proof uses this declaration.
- ProbabilityTheory.integral_id_gaussianRealproof · cited by 6
- AnalyticAt.analyticOrderAt_sub_eq_one_of_deriv_ne_zeroproof · cited by 3
- PeriodPair.eqOn_deriv_weierstrassPExcept_derivWeierstrassPExceptproof · cited by 3
- Real.sin_gt_sub_cubeproof · cited by 2
- AnalyticAt.analyticOrderAt_deriv_add_oneproof · cited by 2
- logDeriv_prod_sineTerm_eq_sum_cotTermproof · cited by 1
- ProbabilityTheory.variance_fun_id_gaussianRealproof · cited by 1
- taylor_integral_remainderproof · cited by 0