Theorems · Theorem · real analysis
deriv_mul
∀ {𝕜 : Type u} [inst : NontriviallyNormedField 𝕜] {x : 𝕜} {𝔸 : Type u_3} [inst_1 : NormedRing 𝔸]
[inst_2 : NormedAlgebra 𝕜 𝔸] {c d : 𝕜 → 𝔸},
DifferentiableAt 𝕜 c x → DifferentiableAt 𝕜 d x → deriv (c * d) x = deriv c x * d x + c x * deriv d x- Defined in
- Mathlib.Analysis.Calculus.Deriv.Mul
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 185 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- NormedRingstatement and proof · cited by 924
- derivstatement · cited by 676
- DifferentiableAtstatement and proof · cited by 617
- HasDerivAt.derivproof · cited by 147
- DifferentiableAt.hasDerivAtproof · cited by 114
- HasDerivAt.mulproof · cited by 20
Cited by2
Results whose statement or proof uses this declaration.
- Derivative.normalizedDerivOfComplex_mulproof · cited by 1
- logDeriv_eqOn_iffproof · cited by 0