Differentiation Of Composite Function Research Articles

Total Differentiation Under Jet Composition

Total differentiation operators as linear vector fields, their flows, invariants and symmetries form the geometry of jet space. In the jet space the dragging of tensor fields obeys the exponential law. The composition of smooth maps induces a composition of jets in corresponding jet spaces. The prolonged total differentiation operators generalize the differentiation of composite function. The relations between Cartan forms under the jet composition are described. MSC (2000): 58A20, 58A40, 28A15.

Differentiation of Multivariable Composite Functions and Bell Polynomials

We generalize the Bell polynomials in order to derive an operational tool for the differentiation of composite functions in several variables. In particular we show a formula that relates the Bell polynomials for multivariable composite functions to the classical ones. Some applications are suggested.