Determine Whether $\mathrm { F } ( x , y , z ) = \left\langle x ^ { 2 } \cos \left( x ^ { 3 } \right) , y e ^ { y ^ { 2 } } , z \sin z \right\rangle$

Essay

Determine whether $\mathrm { F } ( x , y , z ) = \left\langle x ^ { 2 } \cos \left( x ^ { 3 } \right) , y e ^ { y ^ { 2 } } , z \sin z \right\rangle$ is conservative and if so, find a potential function.