How to learn high school mathematics derivatives well.

Learning the basic knowledge of derivative: Limit and derivative are advanced mathematics knowledge in a strict sense, so it will be very difficult for ordinary high school students to learn and master the related knowledge of derivative from the perspective of reasoning and proof.

However, if we regard derivative as a special formula and remember it flexibly, then this part of basic knowledge will become an easier part to master in senior high school mathematical function knowledge.

The application skills of derivative knowledge in mathematics examination: after the derivative knowledge is compressed into the senior high school curriculum, the examination difficulty in the examination is smaller than that in advanced mathematics. Therefore, we only need to master some specific skills to use derivative knowledge flexibly in the exam, and then solve the functional analysis problem in the finale question more efficiently.

The first step is to master the basic knowledge of derivatives.

Trick 1: Derivative is the only criterion to test the changing trend of a function.

In senior high school, there are at least three methods to compare the monotonicity of functions, among which the mirror method and the commercial method are the earliest methods that people contact and are relatively intuitive.

However, these methods are limited to several basic functions that can calculate function values and have known functions, such as parabola of quadratic function and sine curve of trigonometric function. However, for more general functions given by expressions, these methods are basically ineffective-most functions in the finale of the college entrance examination can't compare the sizes in a specific interval by calculating the function values. There is no way to judge the changing trend by piecing together the diagrams of basic functions. Therefore, in essence, the knowledge of function analysis learned in senior one is almost hard to get in the college entrance examination, and the analysis method that can accurately predict the changing trend of general function expressions has only derivatives in senior three.

Therefore, before entering the general review of the college entrance examination, everyone must consciously cultivate their habit of "sublating", and in this part of the knowledge of functional analysis, the first step of sublating is to replace image law and business law with derivatives!

On this basis, we must firmly believe that:

As long as the expression of the function is given, then through some form of derivation, its changing trend will definitely be related to the basic function model we learned in high school, so these problems must be solvable!

However, we need to remind everyone that the process of derivation is essentially a process of expressing known complex functions with a simpler function that can judge the zero characteristic. Therefore, only by fully understanding the monotonicity and zero characteristics of various basic functions in high school textbooks can we really ensure that this sub-question can be answered correctly.

Therefore, the knowledge of function derivation is relatively simple for students who have carefully mastered the basic knowledge of the textbook, but for students who have not understood the basic points of the textbook, even if they have carefully mastered the derivative formula, they may not be able to make corresponding breakthroughs in this part.