Theorems · Theorem · real analysis
deriv_mul_const_field
∀ {𝕜 : Type u} [inst : NontriviallyNormedField 𝕜] {x : 𝕜} {𝕜' : Type u_2} [inst_1 : NormedDivisionRing 𝕜']
[inst_2 : NormedAlgebra 𝕜 𝕜'] {u : 𝕜 → 𝕜'} (v : 𝕜'), deriv (fun y => u y * v) x = deriv u x * v- Defined in
- Mathlib.Analysis.Calculus.Deriv.Mul
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 187 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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
- MulZeroClass.mul_zeroproof · cited by 2,091
- MulZeroClass.zero_mulproof · cited by 1,625
- NormedAlgebrastatement and proof · cited by 1,165
- eq_or_neproof · cited by 1,117
- derivstatement and proof · cited by 676
- DifferentiableAtproof · cited by 617
- NormedDivisionRingstatement and proof · cited by 360
- deriv_zero_of_not_differentiableAtproof · cited by 34
- mul_inv_cancel_right₀proof · cited by 30
- deriv_constproof · cited by 11
- DifferentiableAt.mul_constproof · cited by 5
Cited by4
Results whose statement or proof uses this declaration.
- deriv_div_constproof · cited by 6
- jacobiTheta₂'_functional_equationproof · cited by 1
- logDeriv_mul_constproof · cited by 0
- deriv_mul_const_field'proof · cited by 0