Answer
$\displaystyle y' = \frac{-cosec^{2}x}{(1+cotx)^{2}}$
Work Step by Step
$\displaystyle y = \frac{cotx}{1+cotx}$
$\displaystyle y' = \frac{-(1+cotx)cosec^{2}x - (-cosec^{2}x)cotx}{(1+cotx)^{2}}$
$\displaystyle y' = \frac{-cosec^{2}x -cotx\ cosec^{2}x + cotx\ cosec^{2}x}{(1+cotx)^{2}}$
$\displaystyle y' = \frac{-cosec^{2}x}{(1+cotx)^{2}}$
