Answer
$\lt(1+xy)e^{xy},x^2e^{xy}\gt$
Work Step by Step
$f_x(x,y)=e^{xy}+xy^{xy}$
$f_y(x,y)=x^2e^{xy}$
Gradient vector field of $f$ is: $\lt(1+xy)e^{xy},x^2e^{xy}\gt$
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