Аннотация
The article draws attention to the emergence of new operator operations through the reuse of simple mathematical operations and their application in everyday life, scientific and technical processes. An example of this idea is the fact that arithmetic and geometric progressions known from school mathematics arise from the repetition of simple operations. In addition, noting that the concept of a higher order derivative is a derivative of the multiple use of the derivative method, the final part of the article considers the original problem for a differential equation to determine an unknown function given by a higher order product. Of course, the solution to this problem requires a large number of solving problems from the student, subtle cognitive abilities. For example, a function with an upper limit of a variable integral, the application of the partial integration method to such functions, and other transformations require a great deal of mastery of explanation on the part of the teacher and considerable preparation in mastering the mastery of the student. Note that the purpose of this article is to deepen differential equations and expand the field of application in high school. Therefore, the main task is to describe the methods of integrating differential equations in the pedagogical and methodological base of school mathematics.