  In a recent paper, Adamchik [V.S. Adamchik, On the Hurwitz function for
rational arguments, Appl. Math. Comp. 187 (2007) 3--12] expressed in a closed
form symbolic derivatives of four functions belonging to the class of functions
whose derivatives are polynomials in terms of the same functions. In this
sequel, simple closed-form higher derivative formulae which involve the
Carlitz-Scoville higher order tangent and secant numbers are derived for eight
trigonometric and hyperbolic functions.
