A note on the higher derivatives of the function 1/(exp(x) - 1)
  In this note we compare two formulas for the higher order derivatives of the function 1/(exp(x) -1). We also provide an integral representation for these derivatives and obtain a classical formula relating zeta values and Bernoulli numbers. 
Khristo N. Boyadzhiev (Department of Mathematics and Statistics, Ohio   Northern University, Ada, OH)
math.GM