Theorems · Theorem · real analysis
deriv_comp_add_const
∀ {𝕜 : Type u_1} {F : Type u_2} [inst : NontriviallyNormedField 𝕜] [inst_1 : NormedAddCommGroup F]
[inst_2 : NormedSpace 𝕜 F] (f : 𝕜 → F) (a x : 𝕜), deriv (fun x => f (x + a)) x = deriv f (x + a)Translation in the domain does not change the derivative.
- Defined in
- Mathlib.Analysis.Calculus.Deriv.Shift
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 173 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- add_commproof · cited by 1,535
- derivstatement and proof · cited by 676
- deriv_comp_const_addproof · cited by 3
Cited by6
Results whose statement or proof uses this declaration.
- deriv_comp_sub_constproof · cited by 2
- Real.deriv_Gamma_natproof · cited by 2
- iter_deriv_inv_linearproof · cited by 2
- iteratedDeriv_comp_add_constproof · cited by 2
- Real.hasDerivAt_Gamma_one_halfproof · cited by 1
- Complex.deriv_Gamma_add_oneproof · cited by 1