$(2)(16$ points$)$ Let g$($x$,$y$)=($e$^(-$x$-$y$),$e$^($xy$))$ and f$($u$,$v$)=($u$^(2)+$v$^(2))/($u$^(2)-$v$^(2)).$

$($a$)(4$ points$)$ Calculate h$=$f@g$,$ i$.$e$.$ what is h$($x$,$y$)=$f$($g$($x$,$y$))=?$

$($b$)(12$ points$)$ Use the chain rule to calculate the derivative matrix Dh$($x$,$y$)$ using the

derivative matrices Dg$($x$,$y$)$ and Df$($u$,$v$).$