(%i10) f: 3/T + sum((1/T^2 - exp(-theta(k)/(2*T))/(1 - exp(-theta(k)/(2*T))))*theta(k)/2, k, 1, 3*n-6);
                                              theta(k)
                 3 n - 6                    - --------
                 ====                           2 T
                 \                 1      %e
                  >      theta(k) (-- - ----------------)
                 /                  2           theta(k)
                 ====              T          - --------
                 k = 1                            2 T
                                        1 - %e              3
(%o10)           ---------------------------------------- + -
                                    2                       T
(%i11) diff(f, T);
(%o11)
                                  theta(k)                  theta(k)
3 n - 6                         - --------                - --------
====                                2 T                        T
\                    theta(k) %e               theta(k) %e               2
 >      theta(k) (- ----------------------- - ------------------------ - --)
/                                 theta(k)                  theta(k)      3
====                            - --------                - --------     T
k = 1                  2            2 T          2            2 T    2
                    2 T  (1 - %e          )   2 T  (1 - %e          )
----------------------------------------------------------------------------
                                     2
   3
 - --
    2
   T
(%i12)