I have to prove this equality using index notation (Einstein summation), but I don't know how to proceed from here:
$\nabla(A \cdot B)=A \times (\nabla \times B)+(A \cdot \nabla)B+B \times (\nabla \times A)+(B \cdot \nabla)A$
$\partial_i(a_j b_j)$ -> Product rule
$(\partial_i a_j)b_j+a_j(\partial_i b_j)$ -> What should I do here?
Thank you! All the best.