The steady velocity field in an inviscid fluid of density $1.5$ is given to be $\vec{V} = \left ( y^{2}-x^{2} \right )\hat{i} + \left ( 2xy \right )\hat{j}.$ Neglecting body forces, the pressure gradient at $(x = 1, y = 1)$ is _________________.

1. $10\hat{j}$
2. $20\hat{i}$
3. $-6\hat{i} - 6\hat{j}$
4. $-4\hat{i} - 4\hat{j}$