Find the gradient vector field of the function $f(x,y)=x^2{e}^{2y}+y^2{e}^{2x}$

Which field matches which plot?

$($a$),F^{\text{v}\text{e}\text{c}()}=($:$x,-y$:$)$

$($b$)$ vec$(F)=($:$y,-x$:$)$

Please help with #$2,3$ and show work

Thank you