Let $p(x) = 2^{x}\tan\!\left(x\right)$. 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 $f(x) \cdot g(x)$ of basic functions
D. A quotient $f(x)/g(x)$ of basic functions

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