Answer
${\triangledown}f=(x−y)i+(y−x)j$
Gradient vector field sketch:
Work Step by Step
f(x,y)=12(x−y)2
Using the chain rule of differentiation we have:
$f_x(x,y)=x$
$f_y(x,y)=-y$
Therefore, the gradient vector field of f is:
$(x−y)i+(y−x)j$
Sketch of the gradient vector field:
