#### Answer

$\displaystyle s' = \frac{-2\csc{t}\ \cot{t}}{(1-\csc{t})^{2}}$

#### Work Step by Step

$\displaystyle s = \frac{1+cosect}{1-cosect}$
$\displaystyle s' = \frac{-(1-cosect)cosect\ cot t - (1+cosect)cosect\ cott}{(1-cosect)^{2}}$
$\displaystyle s' = \frac{-cosect\ cott+cosec^{2}t\ cott -cosect\ cott-cosec^{2}t\ cott}{(1-cosect)^{2}}$
$\displaystyle s' = \frac{-2cosect\ cott}{(1-cosect)^{2}}$