Theorems · Theorem · real analysis
HasDerivAt.add
∀ {𝕜 : Type u} [inst : NontriviallyNormedField 𝕜] {F : Type v} [inst_1 : NormedAddCommGroup F]
[inst_2 : NormedSpace 𝕜 F] {f g : 𝕜 → F} {f' g' : F} {x : 𝕜},
HasDerivAt f f' x → HasDerivAt g g' x → HasDerivAt (f + g) (f' + g') x- Defined in
- Mathlib.Analysis.Calculus.Deriv.Add
- Cited by
- 13 results in Mathlib
- Foundations
- Depth 167 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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
- HasDerivAtstatement and proof · cited by 493
- HasDerivAtFilter.addproof · cited by 5
Cited by13
Results whose statement or proof uses this declaration.
- deriv_fun_addproof · cited by 8
- Real.abs_log_sub_add_sum_range_leproof · cited by 4
- InformationTheory.hasDerivAt_klFunproof · cited by 3
- QuadraticMap.hasLineDerivAtproof · cited by 2
- HasFDerivWithinAt.hasLineDerivWithinAtproof · cited by 2
- deriv_addproof · cited by 2
- Real.deriv_tan_sub_idproof · cited by 1
- Complex.hasDerivAt_logTaylorproof · cited by 1
- integral_bilinear_hasLineDerivAt_right_eq_neg_left_of_integrable_aux1proof · cited by 1
- hasDerivAt_gronwallBoundproof · cited by 1
- iteratedDeriv_mul_pow_sub_of_analyticproof · cited by 0
- deriv_riemannZeta_zeroproof · cited by 0