Derivatives of functions of matrix functions via Bell polynomials

作者：Withers Christopher S^*; Nadarajah Saralees

来源：Utilitas Mathematica, 2016, 99: 43-62.

• Chain rule
• Derivatives of a function of a function
• Faa di Bruno
• Multivariate Bell polynomials
• Partial derivatives

Faa di Bruno gave a chain rule for the derivatives of a function of a scalar function of a scalar. It is succinctly expressed in terms of Bell polynomials. We extend this chain rule to give the partial derivatives of a vector (or matrix) function of a vector (or matrix) function up to order twelve. This result is illustrated using over seventy examples including a prominent statistical one.

• 出版日期2016-3