Let h$($x$)=$f$($x$)$g$($x$).$ If f$($x$)=$lnx and g$($x$)=4$x$22$x$+2,$ what is h$($x$)?$

Select the correct answer below:

h$($x$)=1$x$(4$x$2+2$x$2)+$ln$($x$)(8$x$+2)$

h$($x$)=$ln$($x$)(4$x$22$x$+2)+1$x$(8$x$2)$

h$($x$)=$x$(4$x$22$x$+2)+$ln$($x$)(8$x$2)$

h$($x$)=1$x$(4$x$22$x$+2)+$ln$($x$)(8$x$2)$