If f$($x$)=$x$5+$xf$($x$)=$x$5+$x$,$ we know f$($x$)=5$x$4+1$f$($x$)=5$x$4+1.$ If g$($x$)=$x$22$g$($x$)=$x$22,$ we know g$($x$)=2$xg$($x$)=2$x$.$

Which of the following is the derivative of the quotient f$($x$)$g$($x$)$g$($x$)$f$($x$)?$