Is derivative difficult? Is it really hard to take the college entrance examination derivative

1. As far as the high school level is concerned, almost everyone can learn and understand the derivative, don't worry about intelligence, just worry about not thinking carefully, worry about the teacher's poor guidance, and worry about the teacher's distortion. In the O-level test for junior high school students in the Commonwealth and the AP test for middle school students in the United States, the derivative is relatively deep, but it is only limited to the range that middle school students can understand, which is slightly more difficult than that of Chinese high school students.

2. After the introduction of mathematics, it is natural to differentiate, which begins to be mysterious, the general college graduates, in addition to the mathematics department, the physics department, the astronomy department, the meteorology department, the electrical engineering department 、、、and other highly applied majors, the vast majority of college graduates learn calculus, in fact, it is very, very simple, ordinary intelligence is enough. Don't worry, the public calculus course at the university, the general IQ is enough.

3. If you learn deeply, it is a bottomless pit, you may study for a lifetime, or only learn the skin, such as ordinary differential equations, partial differential equations, differential geometry, 、、、 are all part of calculus, proficient in these, beyond the intelligence of the vast majority of college graduates.

Derivatives are actually not that difficult. The key is to memorize the derivative table, and then practice the calculation of some common forms. You can master the derivative more proficiently, this knowledge point is not difficult, the key is to memorize more things.

Derivatives are actually a mathematical one, similar to the basic idea, which is calculus.

Relative. It's still difficult for most people because the mathematical ideas themselves are hard to understand.

Hello, the general derivation, the tangent, the first question of the big question is not difficult, the second question is difficult.

It is not difficult to sort out your thoughts, eat one bite at a time, and solve the problem step by step.

The reciprocal is actually not difficult, as long as you memorize the formula well, almost all derivatives can be solved.

A: It depends on how well you master it.

I think the derivative of the college entrance examination is more difficult. The mathematical derivative of the college entrance examination is the compulsory content and training of our college entrance examination, and the test points account for a lot, and it is not so easy to understand them all, but no matter how the question type changes, it is actually the same, and it has its fixed solution template.

It is actually very important to master the problem solving rules of a type of question, why is the derivative more difficult, because it is often associated with the knowledge of functions, and it is always tested together, so the comprehensive ability of the derivative question type is relatively strong.

You can check what you won't be able to do according to the following;

1. Monotonicity.

The problem of monotonicity of functions is a major application of derivatives, and to solve problems such as monotonicity and range of parameters, it is necessary to solve the inequalities of derivative functions, which often involve solving inequalities with parameters or inequalities with parameters. Since the expression of the function often contains the number of parameter bridges, it is necessary to pay attention to the classification of the parameters and the definition domain of the function when studying the monotonicity of the function.

2. Separation parameter construction method.

Separation parameter refers to the fact that the parameter coefficient can be judged to be positive or negative for the known constant inequality, and the parameter is separated according to the nature of the inequality, so as to obtain an inequality in which one end is a parameter and the other end is a variable, and the problem can be solved by studying the maximum value of the variable inequality.

3. Use derivatives to study tangent problems.

The key is to have tangent abscissa and use three sentences to form a column. Specifically, the problem must appear tangent abscissa, and if there are no tangent coordinates, you must set your own tangent coordinates. Then, use three sentences to column:

The tangent is on the tangent; The tangent point is on the curve; The slope is equal to the derivative. With these three sentences, you can answer 100% of all tangent problems.

4. Application of derivatives in the extrema of functions.

Using the knowledge of derivatives to find the extreme value of a function is a common type of math problem in high school. The general steps to find the extreme value of a function using the derivative are: (1) first find the derivative of the function according to the derivative rule; (2) let the derivative of the function be equal to 0, so that the zero point of the derivative function is solved; (3) the number of zeros of the derivative function is discussed in intervals to obtain the monotonic interval of the function; (4) Judge the extreme point of the function according to the definition of the extreme point, and finally find the extreme value of the function.

The method of arguing and fighting is as follows, carrying the grind.

Please do the divination test:

If we think of the x-cavity beam as u, then y is the composite positive volt function of u. You need to bring Woo Yun 2x in the back

That's right, it's a composite function, and you need to multiply x later, and you're doing it exactly.

This function is a composite function, and the square of x also needs to be derivative, so it should be multiplied by 2x.

<> and differential product of the male head limb celery calendar.

The formula of the basis stuff and differential product of the three-fight banquet bending auspicious leakage angle function is used.

The first horizontal line is the definition of the derivative is converted, if you don't understand the circle, you can look at the definition of the derivative and familiarize yourself with it.

The second horizontal line uses the sum difference product formula: sin -sin =2cos[( 2]sin[( 2], which is converted to argue for things, so that x+δx= ,x= can be used to draw horizontal lines by importing the formula.

Xie Xuan Song teased the answer to Zheng:

Utilize the sum difference product formula.

Of course, derivatives are not difficult, they are the most basic in algebra, and they are also the basis for you to learn advanced mathematics.

It depends on how well you learn, whether it is difficult or not is relative, you are usually serious, practice more, and it is naturally simple! ~~

Derivative is the knowledge of advanced mathematics, you need to use the idea of the limit, the university will open a course in advanced mathematics, of course, if you study mathematics, it is mathematical analysis, then you will talk about the derivative specifically, it will be much more complicated, the key is to understand its concept, this point to understand! Concepts in mathematics are very important, and they must be accurately expressed in mathematical language, otherwise there will be a lot of confusion that cannot be explained.

There are several main aspects to understand the definition of derivative:

1) The derivative is defined as the limit of the quotient between the increment of the dependent variable and the increment of the independent variable when the increment of the independent variable tends to zero.

2) In analytic geometry, it is equivalent to the slope of the tangent of a curve.

3 Applications in physical concepts, such as velocity is the derivative of distance with respect to time, and acceleration is the derivative of velocity with respect to time.

The concept must be understood on the basis of the limit, and it will be easier to understand the definition of the limit first, but don't worry if you don't understand it for a while, the knowledge taught in high school is very superficial, and there is a lot of knowledge that is ignored and given directly to the result, as long as you remember to apply it. After all, it took a long time for so many mathematicians to come up with a strict definition of the limit, so it was so easy to understand, wouldn't it be shameful for them? Go for it.

A derivative is the slope of a function's tangent at a certain point.

The positive or negative of the derivative can determine the monotonicity of a function, and if the derivative is positive in a certain interval, then the function increases singly in that interval.

There is a fixed formula for deriving functions, and they must be ripe.

The importance of learning derivatives well is self-evident, and it is usually the finale of mathematics in the college entrance examination:

The test questions are usually divided into two steps, the first step is simpler, mostly to find functions, monotonic intervals, etc. The main point is to be proficient in derivative formulas, careful calculations, and clear concepts.

The second part is more difficult and has many steps. It is necessary to focus on the overall situation, start with simplicity, write as much as you can, and give up strategically. The second question usually contains:

Conditional transformation: capriciousness, the presence of a variable that makes a condition true, etc. Solution: To clarify the relationship, the parameter a variable x separation into a is the maximum value of the function about g(x).

Applications of derivatives and second derivatives. To use images as a breakthrough, the conceptual and mathematical skills are extremely demanding.

Do more questions, understand more questions, and generalize more.

It is to find the slope, monotonicity, zero range ,..

I don't know which province or city you are taking the college entrance examination.

Take Beijing as an example, half of the college entrance examination derivatives are placed in the third-to-last question, and the score is about 13 points.

So the derivative problem won't be too difficult.

Pay special attention to lnx, a x, loga

x This kind of guidance will do.

First of all, in the derivative problem during the exam, the derivative is mostly in the form of fractions, the denominator is generally constant "0", and the numerator is generally a quadratic function.

Normally, this quadratic function is a quadratic function with coefficients and arguments.

After that, we can start the categorical discussion.

Classification Discussion Point 1: Discuss whether the quadratic coefficient is equal to 0

Of course, if the person who wrote the question was kind, maybe it wouldn't exist.

For example, if the opening is upward, <=0 will increase monotonically on the interval Classification Discussion Point 3: If >0, then you can consider factoring normally No one will let you use the root finding formula. There's no point in taking this test.

Pay attention to the comprehensive application of classification discussion points 2 and 3, and draw a picture, thread the needle (note the negative sign) or directly draw the original function image, so that the probability of error will be lower.

For example, the root is 1 (a+1) and 1 (a-1), and many people will be wrong when discussing the problem of the size of a on (0,1) and a on (1,+infinity).

(1) f’(x)=‘1/x - a/(x-1)^2 = x^2-(2+a)x+1] /x(x-1)^2]

Since the function f(x)=lnx+a (x-1) has an extreme value in (0,1 e), the function is derivable everywhere in this range.

So the derivative of the extreme point is zero.

So the molecule of the derivative x 2-(2+a)x+1 has a solution in the range (0,1 e).

4a+a 2 0 solution gives a -4, or a 0

In addition, it is necessary to ensure that the solution is within (0,1 e), since the axis of symmetry is 1+a2, if a -4 will lead to no solution.

So a 0 and f(1 e) 0 can be solved to a (e-1) 2 e and there is only one solution in (0,1) because the axis of symmetry is to the right of x=1.

2) At (0,1), f(x)<0, and there is only one extreme point, which must be the maximum value, take a=(e-1) 2 e

The extreme point is x1=[2+a- (4a+a2)] 2 =1 e and the maximum value is f(1 e)=-e

In (1, positive infinity)f(x)>0, from the above analysis, it can be seen that there is also a unique and minimum point in this interval taken a=(e-1) 2 e

The extreme point is x2=[2+a+ (4a+a 2)] 2 =e and the minimum value is f(e)=2-1 e

So f(x2)-f(x1)>e+2-1 e

(1) The reciprocal of f(x) is equal to 0, and we get a=(x-1) x, and we get a from negative infinity to (1-e).

Is this calculated by parametric separation? But how do you get it! I'm counting it too... Incomprehensible!