$(10$ points$)$ Differentiate and simplify $f(x)=\frac{e^{2x}-9}{e^{2x}+3}.$

$(14$ points$)$ The demand function for a product is modeled by $p=125e^{-0\mathrm{.}005x}$ where $p$ is the price $($in dollars$)$ and $x$ is the number of units. Find the price that will maximize revenue and the maximum revenue. Verify your solution is a maximum.