Theorems · Theorem · global analysis
hasDerivAt_taylorWithinEval_succ
∀ {E : Type u_2} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] {x₀ x : ℝ} {s : Set ℝ} (f : ℝ → E) (n : ℕ),
HasDerivAt (taylorWithinEval f (n + 1) s x₀) (taylorWithinEval (derivWithin f s) n s x₀ x) xCalculate the derivative of the Taylor polynomial with respect to x.
- Defined in
- Mathlib.Analysis.Calculus.Taylor
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 187 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites42
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
- Realstatement and proof · cited by 25,697
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- Finset.sumproof · cited by 5,195
- mul_oneproof · cited by 3,885
- one_mulproof · cited by 2,841
- add_zeroproof · cited by 2,707
- Nat.cast_oneproof · cited by 2,501
- Finset.sum_congrproof · cited by 2,323
- MulZeroClass.mul_zeroproof · cited by 2,091
- Nat.cast_zeroproof · cited by 1,870
Cited by1
Results whose statement or proof uses this declaration.
- taylor_isLittleOproof · cited by 2