Theorems · Theorem · real analysis
iteratedDeriv_scomp_two
∀ {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},
ContDiffAt 𝕜 2 g (f x) →
ContDiffAt 𝕜 2 f x →
iteratedDeriv 2 (g ∘ f) x = deriv f x ^ 2 • iteratedDeriv 2 g (f x) + iteratedDeriv 2 f x • deriv g (f x)- Cited by
- 0 results in Mathlib
- Foundations
- Depth 197 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites13
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
- ENatstatement · cited by 4,985
- Set.univproof · cited by 3,945
- WithTopstatement · cited by 3,754
- derivstatement · cited by 676
- Set.mem_univproof · cited by 416
- ContDiffAtstatement and proof · cited by 262
- iteratedDerivstatement · cited by 188
- uniqueDiffOn_univproof · cited by 66
- Set.mapsTo_univproof · cited by 55
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