theorem :: FDIFF_8:21

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