Theorems · Theorem · real analysis
iteratedDeriv_scomp_eq_sum_orderedFinpartition
∀ {𝕜 : Type u_1} {E : Type u_2} [inst : NontriviallyNormedField 𝕜] [inst_1 : NormedAddCommGroup E]
[inst_2 : NormedSpace 𝕜 E] {g : 𝕜 → E} {f : 𝕜 → 𝕜} {x : 𝕜} {n : WithTop ℕ∞} {i : ℕ},
ContDiffAt 𝕜 n g (f x) →
ContDiffAt 𝕜 n f x →
↑i ≤ n → iteratedDeriv i (g ∘ f) x = ∑ c, (∏ j, iteratedDeriv (c.partSize j) f x) • iteratedDeriv c.length g (f x)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 196 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- Finset.sumstatement and proof · cited by 5,195
- ENatstatement and proof · cited by 4,985
- WithTopstatement and proof · cited by 3,754
- Finset.univstatement and proof · cited by 3,473
- Finset.prodstatement and proof · cited by 2,356
- Finset.sum_congrproof · cited by 2,323
- ContDiffAtstatement and proof · cited by 262
- iteratedDerivstatement and proof · cited by 188
- OrderedFinpartitionstatement and proof · cited by 61
Cited by1
Results whose statement or proof uses this declaration.
- iteratedDeriv_comp_eq_sum_orderedFinpartitionproof · cited by 0