Explicit expressions for a family of Bell polynomials and derivatives of some functions

Feng Qi, Miao-Miao Zheng

Published 2014-04-27, updated 2014-05-11Version 2

In the paper, the authors first inductively establish explicit formulas for derivatives of the arc sine function, then derive from these explicit formulas explicit expressions for a family of Bell polynomials related to the square function, and finally apply these explicit expressions to find explicit formulas for derivatives of some elementary functions.