  For an arbitrary coordinate system \(x\) the components \(dv^{\,i}_p\) vanish whenever \(v^{\,i}_p\) or \(dx^{\,i}_p\) vanish. Consequently, \(dv^{\,i}_p\) is bi-linear in \(v^{\,i}_p\) and \(dx^{\,i}_p\); that is, 