Curl of a scalar and vector product

 $\nabla \times (f{\vec {A}})$

 $\epsilon _{ijk}\partial _{j}(fA_{k})=\epsilon _{ijk}(\partial _{j}f)A_{k}+\epsilon _{ijk}f\partial _{j}A_{k}$

 $f\nabla \times {\vec {A}}+\nabla f\times {\vec {A}}$