The definition of differential in mathematics: from the function B=f(A), two groups of numbers A and B are obtained. In A, when dx approaches itself, the limit of the function at dx is called the differential of the function at dx, and the central idea of the differential is infinite division.

If the change of the function y =f(x) at point x △y=f(x0+△x)-f(x0) can be expressed as △y=A△x+α(△x),

Where a has nothing to do with △x, and α(△x) is the high-order infinitesimal of △x, then A△x is called the differential of the function y=f(x) at x, and it is denoted as dy, that is, Dy = a △ x, and the function y=f(x) is called differentiable at x..

Extended data:

The differences between the differential and the product are as follows:

1, different generation times:

Differential: As early as the Greek period, human beings began to discuss the concepts of infinity, limit and infinite division. These are the central ideas of calculus; Although there are many loopholes in these discussions from a modern point of view, and sometimes modern people even think that the arguments and conclusions of these discussions are ridiculous, it is undeniable that these discussions are the first step for human beings to develop calculus.

Integral: In the 7th century BC, Thales, an ancient Greek scientist and philosopher, studied the area, volume and length of a ball, which included the idea of calculus.

2. Different mathematical expressions:

Differential: There are some differences in writing between derivative and differential. For example, y'=f(x) is derivative and dy=f(x)dx is differential.

Integral: Let f(x) be the original function of function F(x). We call all primitive functions f(x)+c (c is an arbitrary constant) indefinite integrals of function f(x). The mathematical expression is: if f'(x)=g(x), there is ∫ g.