theorem :: FDIFF_7:33

for Z being open Subset of REAL st Z c= dom (cos * ln) & ( for x being Real st x in Z holds
x > 0 ) holds
( cos * ln is_differentiable_on Z & ( for x being Real st x in Z holds
((cos * ln) `| Z) . x = - ((sin . (ln . x)) / x) ) )