Application of symbolic differentiation for solving of some computational problems

On the example of the Newton’s method of solving of non-linear equations and other similar problems the usage of the symbolic differentiation in the C++ programming language is demonstrated. The proposed approach is based on the metaprogramming of the C++ language, in particular, on expression templates. The problem of solving of a single equation with one variable, of a system of equations with multiple variables, the problem of finding of a minimum of an equation with multiple variables and other similar problems are considered.