theorem :: FDIFF_8:32

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