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.

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The Answer of 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.

Determine Whether F(x,y,z)=⟨x2cos⁡(x3),yey2,zsin⁡z⟩\mathrm { F } ( x , y , z ) = \left\langle x ^ { 2 } \cos \left( x ^ { 3 } \right) , y e ^ { y ^ { 2 } } , z \sin z \right\rangleF(x,y,z)=⟨x2cos(x3),yey2,zsinz⟩

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