Question

Find the gradient field bold upper ffequals=gradient phi∇φ for the potential function phiφequals=x squared y minus y squared xx2y−y2x.

Answer 1

$\varphi(x,y)=x^2y-y^2x\implies\nabla\varphi(x,y)=\mathbf f(x,y)=(2xy-y^2)\,\mathbf i+(y-2xy)\,\mathbf j$