Derivative polynomials and closed-form higher derivative formulae

In a recent paper, Adamchik [1] 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.