Answer
$\frac{dy}{dt}$ = $\frac{csc^{2}(\frac{t}{2})}{[1+cot(\frac{t}{2})]^{3}}$
Work Step by Step
$y$ = $[1+cot(\frac{t}{2})]^{-2}$
$\frac{dy}{dt}$ = $\frac{d}{dt}$$[1+cot(\frac{t}{2})]^{-2}$
$\frac{dy}{dt}$ = $(-2)[1+cot(\frac{t}{2})]^{-3}$ $\frac{d}{dt}$$[1+cot(\frac{t}{2})]$
$\frac{dy}{dt}$ = $(-2)[1+cot(\frac{t}{2})]^{-3}$$[-csc^{2}(\frac{t}{2})]$ $\frac{d}{dt}$($\frac{t}{2})$
$\frac{dy}{dt}$ = $(-2)[1+cot(\frac{t}{2})]^{-3}$$[-csc^{2}(\frac{t}{2})]$($\frac{1}{2})$
$\frac{dy}{dt}$ = $[csc^{2}(\frac{t}{2})]$$[1+cot(\frac{t}{2})]^{-3}$
$\frac{dy}{dt}$ = $\frac{csc^{2}(\frac{t}{2})}{[1+cot(\frac{t}{2})]^{3}}$
