Theorems · Theorem · real analysis
iteratedDeriv_mul
∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {n : ℕ} {x : 𝕜} {𝔸 : Type u_5} [inst_1 : NormedRing 𝔸]
[inst_2 : NormedAlgebra 𝕜 𝔸] {f g : 𝕜 → 𝔸},
ContDiffAt 𝕜 (↑n) f x →
ContDiffAt 𝕜 (↑n) g x →
iteratedDeriv n (f * g) x =
∑ i ∈ Finset.range (n + 1), ↑(n.choose i) * iteratedDeriv i f x * iteratedDeriv (n - i) g x- Cited by
- 2 results in Mathlib
- Foundations
- Depth 209 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.
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- Finset.sumstatement · cited by 5,195
- ENatstatement · cited by 4,985
- WithTopstatement · cited by 3,754
- Finset.sum_congrproof · cited by 2,323
- Finset.rangestatement and proof · cited by 1,341
- NormedAlgebrastatement and proof · cited by 1,165
- NormedRingstatement and proof · cited by 924
- Nat.choosestatement and proof · cited by 494
- Set.mem_univproof · cited by 416
- ContDiffAtstatement and proof · cited by 262
- iteratedDerivstatement · cited by 188
Cited by2
Results whose statement or proof uses this declaration.
- UpperHalfPlane.qExpansion_mulproof · cited by 1
- iteratedDeriv_fun_mulproof · cited by 0