Determine Whether or Not $\mathbf { F } ( x , y ) = ( y \cos x - \cos y ) \mathbf { i } + ( \sin x + x \sin y ) \mathbf { j }$

Essay

Determine whether or not $\mathbf { F } ( x , y ) = ( y \cos x - \cos y ) \mathbf { i } + ( \sin x + x \sin y ) \mathbf { j }$ is a conservative vector field. If it is, find a function f such that $\mathbf { F } = \nabla f$