∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type u_2} [inst_1 : NormedAddCommGroup E]
  [inst_2 : NormedSpace 𝕜 E] {𝔸 : Type u_5} [inst_3 : NormedRing 𝔸] [inst_4 : NormedAlgebra 𝕜 𝔸] {a b : E → 𝔸}
  {a' b' : E →L[𝕜] 𝔸} {x : E},
  HasStrictFDerivAt a a' x →
    HasStrictFDerivAt b b' x → HasStrictFDerivAt (a * b) (a x • b' + MulOpposite.op (b x) • a') x