Answer
See the explanation below.
Work Step by Step
$\bf{F}$ defines a vector field such as: $\bf{F}=Pi+Qj$ which is conservative iff the following conditions satisfies, thus
$\frac{\partial P}{\partial y}=\frac{\partial Q}{\partial x}$
The vector field $\bf{F}$ on $R^3$ is conservative iff $\bf{curlF}=0$. This implies that $F$ is conservative when the partial derivatives satisfy the condition such that: $\frac{\partial P}{\partial y}=\frac{\partial Q}{\partial x}$.
