And derivative, also called derivative function value. Also known as WeChat quotient, it is an important basic concept in calculus. When the independent variable x of the function y=f(x) generates an increment δ x at the point x0, if there is a limit a in the ratio of the increment δ y of the function output value to the increment δ x of the independent variable when δ x tends to 0, then A is the derivative at x0, which is denoted as f'(x0) or df(x0)/dx.

Development course of derivative products:

1, origin:

Around 1629, the French mathematician Fermat studied the method of tangent curve and extreme value of function; 1637 or so, he wrote a manuscript "the method of finding the maximum value and the minimum value". When doing tangent, he constructed the difference f(A+E)-f(A) and found that the factor e is what we call the derivative f'(A).

2. Development:

/kloc-the development of productivity in the 0/7th century promoted the development of natural science and technology. On the basis of predecessors' creative research, great mathematicians Newton and Leibniz began to study calculus systematically from different angles. Newton's calculus theory is called "flow number". He called the variable flow and the rate of change of the variable flow number, which is equivalent to what we call derivative.

Newton's major works on "Flow Number Theory" include Finding the Area of Curved Polygon, Calculation Method Using Infinite Polynomial Equation, Flow Number Theory and Infinite Series. The essence of stream number theory is summarized as follows: his emphasis is on univariate function, not multivariate equation; It lies in the composition of the ratio of the change of independent variables to the change of functions; The most important thing is to determine the limit of this ratio when the change tends to zero.