theorem :: FDIFF_9:30

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