Theorems · Theorem · real analysis
deriv_const_mul_field
∀ {𝕜 : Type u} [inst : NontriviallyNormedField 𝕜] {x : 𝕜} {𝕜' : Type u_2} [inst_1 : NormedDivisionRing 𝕜']
[inst_2 : NormedAlgebra 𝕜 𝕜'] {v : 𝕜 → 𝕜'} (u : 𝕜'), deriv (fun y => u * v y) x = u * deriv v xA variant of deriv_const_mul without differentiability assumption when the scalar
multiplication is by division ring elements.
- Defined in
- Mathlib.Analysis.Calculus.Deriv.Mul
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 176 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.
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- NormedAlgebrastatement and proof · cited by 1,165
- derivstatement · cited by 676
- NormedDivisionRingstatement and proof · cited by 360
- derivWithin_const_mul_fieldproof · cited by 1
Cited by5
Results whose statement or proof uses this declaration.
- deriv_const_mul_field'proof · cited by 5
- Polynomial.deriv_gaussian_eq_hermite_mul_gaussianproof · cited by 1
- logDeriv_const_mulproof · cited by 1
- Real.iter_deriv_rpow_constproof · cited by 1
- jacobiTheta₂'_functional_equationproof · cited by 1