Theorems · Theorem · real analysis
deriv_fun_add
∀ {𝕜 : Type u} [inst : NontriviallyNormedField 𝕜] {F : Type v} [inst_1 : NormedAddCommGroup F]
[inst_2 : NormedSpace 𝕜 F] {f g : 𝕜 → F} {x : 𝕜},
DifferentiableAt 𝕜 f x → DifferentiableAt 𝕜 g x → deriv (fun y => f y + g y) x = deriv f x + deriv g x- Defined in
- Mathlib.Analysis.Calculus.Deriv.Add
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 172 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- derivstatement · cited by 676
- DifferentiableAtstatement and proof · cited by 617
- HasDerivAt.derivproof · cited by 147
- DifferentiableAt.hasDerivAtproof · cited by 114
- HasDerivAt.addproof · cited by 13
Cited by8
Results whose statement or proof uses this declaration.
- ProbabilityTheory.integral_id_gaussianRealproof · cited by 6
- Real.deriv_qaryEntropyproof · cited by 6
- AkraBazziRecurrence.eventually_deriv_one_add_smoothingFnproof · cited by 2
- Real.deriv2_qaryEntropyproof · cited by 2
- DifferentiableAt.deriv_comp_add_smulproof · cited by 2
- Real.deriv_binEntropyproof · cited by 2
- AkraBazziRecurrence.isLittleO_deriv_one_add_smoothingFnproof · cited by 1
- deriv_riemannZeta_eq_neg_inv_sub_sq_addproof · cited by 1