Determine whether or not $\mathbf { F } ( x , y ) = \left( y e ^ { x y } + 4 x ^ { 3 } y \right) \mathbf { i } + \left( x e ^ { x y } + x ^ { 4 } \right) \mathbf { j }$ is a conservative vector field. If it is, find a function f such that $\mathbf { F } = \nabla f$ .

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The Answer of Determine whether or not $\mathbf { F } ( x , y ) = \left( y e ^ { x y } + 4 x ^ { 3 } y \right) \mathbf { i } + \left( x e ^ { x y } + x ^ { 4 } \right) \mathbf { j }$ is a conservative vector field. If it is, find a function f such that $\mathbf { F } = \nabla f$ .

Determine Whether or Not F(x,y)=(yexy+4x3y)i+(xexy+x4)j\mathbf { F } ( x , y ) = \left( y e ^ { x y } + 4 x ^ { 3 } y \right) \mathbf { i } + \left( x e ^ { x y } + x ^ { 4 } \right) \mathbf { j }F(x,y)=(yexy+4x3y)i+(xexy+x4)j

Determine Whether or Not $\mathbf { F } ( x , y ) = \left( y e ^ { x y } + 4 x ^ { 3 } y \right) \mathbf { i } + \left( x e ^ { x y } + x ^ { 4 } \right) \mathbf { j }$