∇ × ( f A → ) {\displaystyle \nabla \times (f{\vec {A}})}
ϵ i j k ∂ j ( f A k ) = ϵ i j k ( ∂ j f ) A k + ϵ i j k f ∂ j A k {\displaystyle \epsilon _{ijk}\partial _{j}(fA_{k})=\epsilon _{ijk}(\partial _{j}f)A_{k}+\epsilon _{ijk}f\partial _{j}A_{k}}
f ∇ × A → + ∇ f × A → {\displaystyle f\nabla \times {\vec {A}}+\nabla f\times {\vec {A}}}
In the book,
M → × ∇ f = f ∇ × M → − ∇ × ( f M → ) {\displaystyle {\vec {M}}\times \nabla f=f\nabla \times {\vec {M}}-\nabla \times (f{\vec {M}})}
