Find $$z$/$x and $$z$/$y$.$

$($a$)$z $=$ f$($x$)$g$($y$)$

$$z$/$x$$z$/$y

$01$f$\text{'}($x$)$g$\text{'}($y$)$f$\text{'}($x$)$g$($y$)$f$($x$)$g$\text{'}($y$)$f$\text{'}($x$)$g$\text{'}($y$)$none of the above

$01$f$\text{'}($x$)$g$\text{'}($y$)$f$\text{'}($x$)$g$($y$)$f$($x$)$g$\text{'}($y$)$f$\text{'}($x$)$g$\text{'}($y$)$none of the above

$($b$)$z $=$ f$($xy$)$

$$z$/$x$$z$/$y

$01$f$\text{'}($x$)$f$($y$)$f$($x$)$f$\text{'}($y$)$xf$\text{'}($xy$)$yf$\text{'}($xy$)$xyf$\text{'}($xy$)$none of the above

$01$f$\text{'}($x$)$f$($y$)$f$($x$)$f$\text{'}($y$)$xf$\text{'}($xy$)$yf$\text{'}($xy$)$xyf$\text{'}($xy$)$none of the above

$($c$)$z $=$ f$($x$/$y$)$

$$z$/$x$$z$/$y

$01$f$\text{'}($x$/$y$)/$xf$\text{'}($x$/$y$)/$y$$yf$\text{'}($x$/$y$)/$x$2$xf$\text{'}($x$/$y$)/$y$2$none of the above

$01$f$\text{'}($x$/$y$)/$xf$\text{'}($x$/$y$)/$y$$yf$\text{'}($x$/$y$)/$x$2$xf$\text{'}($x$/$y$)/$y$2$none of the above