Suppose k k is a field of characteristic 0 and k [ n ] = k [ x 1 , … , x n ] {k^{[n]}} = k[{x_1}, \ldots ,{x_n}] . If u i {u_i} , f j ∈ k [ n ] {f_j} \in {k^{[n]}} for 1 ⩽ i ⩽ n 1 \leqslant i \leqslant n , 1 ⩽ j ⩽ m 1 \leqslant j \leqslant m , u = ( u 1 , … , u n ) u = ({u_1}, \ldots ,{u_n}) , the f j {f_j} are relatively prime, and each f j u {f_j}u is conservative, then u u is conservative and ( f 1 , … , f m ) ({f_1}, \ldots ,{f_m}) is unimodular. Given any u u with | J ( u ) | = 1 \left | {J(u)} \right | = 1 , then each derivation ∂ / ∂ u i \partial /\partial {u_i} , has divergence 0. If D : k [ n ] → k [ n ] D:{k^{[n]}} \to {k^{[n]}} is a k k -derivation with kernel of dimension n n - − 1 - 1 , then there exists a g g so that g D gD has divergence 0.