$5\mathrm{.}2$A cloud engineer is analysing the average CPU usage per user for a machine learning service, where the function models the usage $,$f$($x$)=$ex$$xf$($x$)=$exx with $$representing the number of simultaneous user requests. To understand how the per$-$user CPU demand changes as user load increases, the engineer needs to determine the slope of the tangent line to the function at$$x$=4$x$=4.$

Calculate the slope of the tangent line to$$f$($x$)=$ex$$xf$($x$)=$exx$$at the point$$x$=4$x$=4.$

$(6$ Marks$)$