Explicit expressions for a family of Bell polynomials and derivatives of   some functions
  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. 
Feng Qi and Miao-Miao Zheng
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