By attempting to find a V such thatF= $\displaystyle - \nabla V$ in each case, find which of the following vector force fields are conservative, and obtain an appropriate potential energy function $\displaystyle V$ when it exists.

(i)F$\displaystyle (x, y, z)$ = $\displaystyle 3x^2yz$i$\displaystyle + (x^3z - cos y)$j$\displaystyle - x^3y$k

(ii)F$\displaystyle (x, y, z)$ = $\displaystyle (2xyz^2 - 6xyze^{x^2yz})$i$\displaystyle + (x^2z^2 - 3x^2ze^{x^2yz})$j$\displaystyle + (2x^2yz - 3x^2ye^{x^2yz})$k.