Let p$($x$)=2$xtan$($x$).$ Which of the following best describes its fundamental algebraic structure?

A$.$ A composition f$($g$($x$))$ of basic functions

B$.$ A sum f$($x$)+$g$($x$)$ of basic functions

C$.$ A product f$($x$)$g$($x$)$ of basic functions

D$.$ A quotient f$($x$)/$g$($x$)$ of basic functions

Compute the derivative p$($x$).$

p$($x$)=$

$2$xln$(2)$sec$2($x$)$