theorem :: FDIFF_9:45

for Z being open Subset of REAL st Z c= dom (cot (#) cosec) holds
( cot (#) cosec is_differentiable_on Z & ( for x being Real st x in Z holds
((cot (#) cosec) `| Z) . x = (- ((1 / ((sin . x) ^2)) / (sin . x))) - (((cot . x) * (cos . x)) / ((sin . x) ^2)) ) )