theorem :: FDIFF_9:31

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