Electric Field from Electric Potential

If the electric potential is given by (\chi=cxy), calculate the electric field.

Discussion:

$$ E_x=-\frac{\partial\chi}{\partial x}=-cy$$
$$ E_y=\frac{\partial \chi}{\partial y}=-cx$$
Hence electric field $$ \vec{E}=-c(y\hat{i}+x\hat{j})$$