The Faa di Bruno formula and determinant identities

The Faa di Bruno formula on higher derivatives of composite functions and formal power series iteration is applied to the combinatorial determinant evaluation. Several determinant identities on composite function derivations and formal power series iterations, as well as their weighted versions, are established. They contain, as particular cases, the determinant evaluations due to Mina (Mina, L., 1905, Formule generali delle successive d'una funzione espresse mediante quelle della sua inversa. Giornale di Matematiche , 43 , 196-212.), Kedlaya (Kedlaya, K.S., 2000, Another combinatorial determinant. Journal of Combinatorial Theory (A) , 90 , 221-223.), and Wilf (Wilf, H.S., A combinatorial determinant. http://www.cis.upenn.edu/similar to wilf.).