$$(x \times { y }^{ -y } +y { x }^{ -x } )( { x }^{ -(x+1) } + { y }^{ -(y+1) } )$$
$x^{-2x-1}y^{-2y-1}\left(x^{x+1}+y^{y+1}\right)^{2}$
$-\frac{2\ln(x)}{x^{x}y^{y}}-\frac{2}{x^{x}y^{y}}-2y\ln(x)x^{-2x-1}-yx^{-2x-2}-2yx^{-2x-1}+y^{-2y-1}$
