1. The problem statement, all variables and given/known data prove, ∇x(ψv)=ψ(∇xv)-vx(∇ψ) using levi civita symbol and tensor notations 2. Relevant equations εijkεimn=δjnδkm-δknδjm 3. The attempt at a solution i tried for nth component εnjk (d/dxj)εklm ψl vm εknjεklm (d/dxj) ψl vm using εijkεimn=δjnδkm-δknδjm i got, (d/dxj)ψn vj - (d/dxj)ψj vn But, i can't go further. I think only one simple step is left to show it is equal to the right hand side of the given identity. But how?