Values of the derivatives of the cotangent at rational multiples of π

By elementary arguments, we deduce closed-form expressions for the values of all derivatives of the cotangent function at rational multiples of ππ. These formulae are considerably simpler than similar ones which were found in a different manner by Kölbig. Also, we show that the values of cot(n)(πx)cot(n)(πx), n∈Nn∈N, at x=12,13,23,14,34,16 and 56 are expressible in terms of the values of the Bernoulli polynomials alone.