Theorems · Theorem · real analysis
iter_deriv_inv_linear
∀ {𝕜 : Type u} [inst : NontriviallyNormedField 𝕜] (k : ℕ) (c d : 𝕜),
(deriv^[k] fun x => (c * x + d)⁻¹) = fun x => (-1) ^ k * ↑k.factorial * c ^ k * (c * x + d) ^ (-1 - ↑k)- Defined in
- Mathlib.Analysis.Calculus.Deriv.ZPow
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 193 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.
Cites36
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
- 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
- zero_addproof · cited by 2,366
- MulZeroClass.mul_zeroproof · cited by 2,091
- MulZeroClass.zero_mulproof · cited by 1,625
- add_commproof · cited by 1,535
- pow_zeroproof · cited by 1,094
- sub_zeroproof · cited by 938
- pow_oneproof · cited by 894
Cited by2
Results whose statement or proof uses this declaration.
- eqOn_iteratedDeriv_cotTermproof · cited by 1
- iter_deriv_inv_linear_subproof · cited by 1