∀ {𝕜 : Type u} [inst : NontriviallyNormedField 𝕜] {F : Type v} [inst_1 : NormedAddCommGroup F]
  [inst_2 : NormedSpace 𝕜 F] {f₁ : 𝕜 → F} {f₁' : F} {L : Filter (𝕜 × 𝕜)} {G : Type w} [inst_3 : NormedAddCommGroup G]
  [inst_4 : NormedSpace 𝕜 G] {f₂ : 𝕜 → G} {f₂' : G},
  HasDerivAtFilter f₁ f₁' L → HasDerivAtFilter f₂ f₂' L → HasDerivAtFilter (fun x => (f₁ x, f₂ x)) (f₁', f₂') L