Theorems · Theorem · real analysis
HasDerivAt.const_add
∀ {𝕜 : Type u} [inst : NontriviallyNormedField 𝕜] {F : Type v} [inst_1 : NormedAddCommGroup F]
[inst_2 : NormedSpace 𝕜 F] {f : 𝕜 → F} {f' : F} {x : 𝕜} (c : F),
HasDerivAt f f' x → HasDerivAt (fun x => c + f x) f' xAlias of the reverse direction of hasDerivAt_const_add_iff.
- Defined in
- Mathlib.Analysis.Calculus.Deriv.Add
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 168 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 · cited by 493
- hasDerivAt_const_add_iffproof · cited by 1
Cited by10
Results whose statement or proof uses this declaration.
- hasDerivAt_circleMapproof · cited by 3
- Real.hasDerivAt_half_log_one_add_div_one_sub_sub_sum_rangeproof · cited by 2
- intervalIntegral.integral_unitInterval_deriv_eq_subproof · cited by 2
- hasDerivAt_circleAverage_herglotzRieszKernel_smulproof · cited by 1
- Convex.taylor_approx_two_segmentproof · cited by 1
- deriv2_sqrt_mul_logproof · cited by 1
- HasDerivAt.comp_const_addproof · cited by 1
- integral_mul_cpow_one_add_sqproof · cited by 1
- hasDerivAt_gronwallBoundproof · cited by 1
- Real.hasDerivAt_sigmoidproof · cited by 1