Derivative is a basic concept in college entrance examination mathematics, which refers to the rate of change of a function at a certain point, that is, the slope at that point. In practical applications, derivatives are often used to solve the extreme and maximum values of equations, and to describe the changing laws in physics, chemistry and other fields. Therefore, mastering the concept and application method of derivative is very important for the study and research in mathematics and science-related fields.

There are many ways to calculate derivatives, among which the definition of limit is often used to solve them. According to the definition of limit, if the derivative of a function exists at a certain point, then its derivative at that point is equal to the limit approached by the ratio of the function value at that point to the slight change of the function value. If the derivative of a function does not exist at a certain point, that point is called the nondifferentiable point of the function. By gradually mastering the calculation method of derivative, the understanding and calculation ability of function can be improved.

Derivative is widely used in advanced mathematics and various practical applications. For example, in the economic and financial fields, the derivative of the solution function can describe the changing trend of market prices; In natural science, derivatives can be used to analyze the tangents of curves and the physical meanings of velocity and acceleration. In the field of engineering technology, derivative can be used to describe the changing law of sound, electromagnetic wave and light. Therefore, the application of learning derivative not only helps to deepen academic theory, but also helps us to better understand and master the relevant knowledge of practical application.