Compute the curl:

Compute the divergence:

A conservative vector field has zero curl, which is not the case here, so
is not conservative.
We can also employ the same method as I showed in an earlier question of yours [28193504]. We want to find a scalar function
whose gradient is
, so


However, there is no function
that depends only on
and
that satisfies this partial differential equation; to wit, we cannot eliminate
. So no such
exists.