Theorems · Theorem · real analysis
iteratedDerivWithin_comp_two
∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {g f : 𝕜 → 𝕜} {s t : Set 𝕜} {x : 𝕜},
ContDiffWithinAt 𝕜 2 g t (f x) →
ContDiffWithinAt 𝕜 2 f s x →
UniqueDiffOn 𝕜 t →
UniqueDiffOn 𝕜 s →
x ∈ s →
Set.MapsTo f s t →
iteratedDerivWithin 2 (g ∘ f) s x =
iteratedDerivWithin 2 g t (f x) * derivWithin f s x ^ 2 +
derivWithin g t (f x) * iteratedDerivWithin 2 f s x- Cited by
- 1 results in Mathlib
- Foundations
- Depth 197 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- NontriviallyNormedField
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- ENatstatement · cited by 4,985
- WithTopstatement · cited by 3,754
- mul_commproof · cited by 2,262
- Set.MapsTostatement and proof · cited by 732
- ContDiffWithinAtstatement and proof · cited by 283
- derivWithinstatement and proof · cited by 258
- UniqueDiffOnstatement and proof · cited by 215
- iteratedDerivWithinstatement and proof · cited by 122
- iteratedDerivWithin_scomp_twoproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- iteratedDeriv_comp_twoproof · cited by 0