Theorems · Theorem · real analysis
HasDerivAt.const_smul
∀ {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} {R : Type u_2} [inst_3 : Monoid R]
[inst_4 : DistribMulAction R F] [SMulCommClass 𝕜 R F] [ContinuousConstSMul R F] (c : R),
HasDerivAt f f' x → HasDerivAt (c • f) (c • f') x- Defined in
- Mathlib.Analysis.Calculus.Deriv.Mul
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 169 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- Monoidstatement and proof · cited by 3,887
- SMulCommClassstatement and proof · cited by 1,927
- ContinuousConstSMulstatement and proof · cited by 832
- DistribMulActionstatement and proof · cited by 584
- HasDerivAtstatement and proof · cited by 493
- HasDerivAtFilter.const_smulproof · cited by 3
Cited by7
Results whose statement or proof uses this declaration.
- HasLineDerivWithinAt.smulproof · cited by 3
- deriv_const_smulproof · cited by 2
- hasDerivAt_circleAverage_herglotzRieszKernel_smulproof · cited by 1
- intervalIntegral.hasDerivAt_integral_of_dominated_loc_of_deriv_leproof · cited by 1
- intervalIntegral.hasDerivAt_integral_of_dominated_loc_of_lipproof · cited by 0
- deriv_fun_const_smulproof · cited by 0
- HasDerivAt.fun_const_smulproof · cited by 0