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 tangent, he constructed the difference f(A+E)-f(A) and found that the factor e is what we now call the derivative f'(A).
(b)1"flow counting" widely used in the 7th century.
/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.
(c)19th century derivative-gradually mature theory
1750, D'Alembert put forward a viewpoint about derivative in the fourth edition of Encyclopedia published by French Academy of Sciences, which can be simply expressed by modern symbols: {dy/dx)=lim(oy/ox).
In 1823, Cauchy defined the derivative in his Introduction to Infinitesimal Analysis: If the function y=f(x) is continuous between two given boundaries of the variable X, and we specify a value for such a variable contained between these two different boundaries, then this variable will get an infinitesimal increment.
After 65438+ 1960' s, Wilstrass created ε-δ language, which restated various types of limits in calculus, and the definition of derivative obtained today's universal form.