theorem :: FDIFF_8:20

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