Theorems · Theorem · real analysis
deriv_const_smul
∀ {𝕜 : Type u} [inst : NontriviallyNormedField 𝕜] {F : Type v} [inst_1 : NormedAddCommGroup F]
[inst_2 : NormedSpace 𝕜 F] {f : 𝕜 → 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), DifferentiableAt 𝕜 f x → deriv (c • f) x = c • deriv f x- Defined in
- Mathlib.Analysis.Calculus.Deriv.Mul
- Cited by
- 2 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.
Cites12
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
- derivstatement · cited by 676
- DifferentiableAtstatement and proof · cited by 617
- DistribMulActionstatement and proof · cited by 584
- HasDerivAt.derivproof · cited by 147
- DifferentiableAt.hasDerivAtproof · cited by 114
- HasDerivAt.const_smulproof · cited by 7
Cited by2
Results whose statement or proof uses this declaration.
- Derivative.normalizedDerivOfComplex_smulproof · cited by 2
- logDeriv_eqOn_iffproof · cited by 0