Theorems · Theorem · real analysis
deriv_const_smul_field
∀ {𝕜 : Type u} [inst : NontriviallyNormedField 𝕜] {F : Type v} [inst_1 : NormedAddCommGroup F]
[inst_2 : NormedSpace 𝕜 F] {x : 𝕜} {𝕝 : Type u_3} [inst_3 : DivisionSemiring 𝕝] [inst_4 : Module 𝕝 F]
[SMulCommClass 𝕜 𝕝 F] [ContinuousConstSMul 𝕝 F] (c : 𝕝) (f : 𝕜 → F), deriv (c • f) x = c • deriv f xA variant of deriv_const_smul without differentiability assumption when the scalar
multiplication is by division ring elements.
- Defined in
- Mathlib.Analysis.Calculus.Deriv.Mul
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 175 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Modulestatement and proof · cited by 20,661
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- Set.univproof · cited by 3,945
- SMulCommClassstatement and proof · cited by 1,927
- ContinuousConstSMulstatement and proof · cited by 832
- derivstatement · cited by 676
- derivWithinproof · cited by 258
- DivisionSemiringstatement and proof · cited by 216
- derivWithin_const_smul_fieldproof · cited by 5
Cited by1
Results whose statement or proof uses this declaration.
- deriv_const_smul'proof · cited by 0