Differentiate each function:

$($a$)f(x)=\frac{e^{3x}-e^{-3x}}{e^{3x}+e^{-3x}}$

$($f$)M(x)={\displaystyle \underset{0}{\overset{x}{}}}\frac{arctant}{\sqrt[\phantom{2}]{t^2+1}}dt$

$($b$)g(x)=sin(arctan(\frac{x}{\sqrt[\phantom{2}]{25-x^2}}))$

$($g$)N(x)=(sinx{)}^x$

$($c$)h(x)=ln(cscx+cotx)$

$($h$)O(x)=x{3}^{x-1}$

$($d$)k(x)=\underset{n}{lim}(1+\frac{1}{n}{)}^{nx}$

$($i$)p(x)=(e^{2x}+e^{-2x}{)}^2$

$($j$)q(x)=(5x{)}^x$

$($e$)l(x)=ln(\frac{x^2-1}{x^2+1})$