Pochidna folding function synopsis. Lesson "lost folding function". III. Updating basic knowledge

Lesson type: combinations

coverage:

- the formulation of the understanding of the folding function;

Formation vmіnnya is known for the rule of lost folding function;

Adding to the algorithm for storing the rules for knowing the obsolete folding function in the case of virtual attachments.

developing:

Razvivati clever uzagalnyuvati, systematize on the basis of porvnyannya, robiti visnovok;

Razvivati naochno-dіve I creative uyavu;

Development of educational interest.

Vikhovna:

Vykhovannya of the grandfathering before initial pratsi, Will and ease of use for achieving endurance results with existing old folding functions;

Formation is rational;

Vikhovannya amicable presentation between students during the lesson.

The student is guilty of the nobility:

the understanding of the folding function, the rule of knowledge її pohіdnoї.

The student is guilty of:

I know for the rule that the folding function is lost;

Interdisciplinary links: physics, geometry, economics.

Equipment for the lesson: a multimedia projector, a magnetic board, a good board, a cradle, a distribution material before the lesson.

Lesson plan:

Obviously, learn a lesson and motivation for the initial activity - 3 min.

Reconstruction of the home office - 5 min (frontal reversal, self-control).
All-purpose conversion of knowledge - 10 min (frontal of the robot, self-control).
Preparation before mastering (vivchennya) new initial material through the repetition and actualization of basic knowledge - 5 min (problematic situation).
Assignment of new knowledge - 15 min
Initial understanding and intelligence of the new material - 20 min (frontal robot: one student shows the butt on the butt, and is shown in zoshits).
Closing of new knowledge - 15 min (robot self-test - test in two versions, with differentiated employees).
Information about homework, instructions about the year's office - 2 min.
Leading the lesson in the lesson, reflection - 5 min.

I. Go to the lesson: Knowing the lesson, creating the lesson plan, motivation for the initial activity:

Revise the preparation of the classroom and the readiness of the students before the lesson, depending on the day.

Apparently, this is a trivial robot on the basis of "Pochіdna funktsії".

II. Perevirk homework.

On the booths, put on the usual funky functions:

5) at point x = 0.

Vidpovidi projected on a multimedia projector.

Students individually revise their views and put their (self-control) score on the control sheet. A skin student has a control sheet, assessment criterion for home robot check the sheet in the handout before the lesson

control sheet

Viclikati to the student's board to show the design of the solution to the butt No. 5 with a commentary of the vikonanikh robot.

Respect for the correct solution and correct design of the home butt stock No. 5.

III. All-purpose conversion of knowledge.

Gra "Mathematical Lotto" - a revision of the knowledge of the rules of differentiation, tables of old ones.

A special envelope of leather pairs of students will have a set of cards (10 cards in total). Tse - formulas. Є The first set of cards. Price - card-views, which are larger, as well as in the middle of the views and the prompts. The student will know the name of the card, and the card (view) is drawn with the corresponding number in the special card. Students work in pairs, to assess one by one, list the assessments in the control sheet according to the criterion: "5" - the meaning of 9-10 formulas; "4" - means 7-8 formulas; "3" - means 5-6 formulas; "2" is less than 5 formulas.

Ide revision and assessment of knowledge of formulas on magnetic dosages. In the case of the correct views on the magnetic backs and backs of the cards-views, create a great picture, as if to play the whole group. The numbers in the special cards are assigned with the numbers of the formula cards. As soon as you open the magnetic field of view from the vortex side, then all the cards as a whole will make the picture.

IV. Preparation before (mastering) the introduction of new material through the repetition and actualization of basic knowledge.

Statement of a problem situation: know the lost function ;

In the past lessons, we came across the knowledge of old elementary functions. functions folding. Do I know old folding functions?

So, what is my fault for this year?

[For the familiar foldable functions.]

Students formulate the topic themselves and start the lesson, the weeklays will write down the topic in docs, and students - in zoshita.

Istorichna dovidka, a link with the future professional performance.

V. Conquest of new knowledge.

Show on the basis of the knowledge of old functions: ;

Virishit butt:

Vi. Initial understanding and intelligence of the new material.

Repeat the algorithm of the familiar folding function;

Virishiti put it on:

4) ;

Vii. Secure new knowledge for additional test for options.

Head of differentiation tests: butt z № 1-3 be rated "3", up to № 4 - on "4", all five butts - on "5".

Students check out and change the view one by one for the additional multimedia and put the score one to one (vzamokrol) in the control sheet.

Option 1.

Know the lost functions. (A., V., S. - відповіді)



1
2
3
4
5
4
5

Danish lesson є vivchennya lesson news by those... Presents a rosette to the lesson to open the methodical approach to the introduction of the folding function, the algorithm for calculating the old. The development is intended for conducting lessons in the middle of the 1st year students to establish the level of professional education.

Zavantazhiti:

Front view:

Suitable for folding function

tsіlі: 1) Illumination - formulate an understanding of the folding function, learn the algorithm for calculating the old folding function, showing it when calculating the old.

2) development - promoting development is less logical and reasoned by mirkuvati, vikoristovuyu uzagalnennya, analysis, adaptation in vivchenn_ obhidnogo folding function.

3) vikhovna - vyhovuvati sparing in the course of the development of mathematical deposits, to continue the formation of self-assessment in the presence of differentiated knowledge, to advance interest in mathematics.

Possession: table of older children, presentation before the lesson.

Lesson outline:

I. AZ.

1.mobilecob (setting up a robot at the urotsi).

2. The robot sleeps with the method of updating the basic knowledge.

3. The revision of the home staff with the motivation for the introduction of new material.

4. Delivery of personnel of the 1st stage and the setting of offensive tasks.

II. FNZ і SD.

Heuristic conversation is based on the introduction of the concept of folding function.
The frontal robot is asleep with the method of fastening the folding function.
According to the teacher the algorithm for calculating the obsolete folding function.
The primary fixation to the algorithm for calculating the lean folding function is frontal.
Pidsumkiv stage II and setting up the building on the offensive.

III. Fun.

1. We will learn the solution to the management based on the algorithm for calculating the lean folding function of the frontal plate.

2. The robot is differentiated according to the revision of the building with a slightly different frontal reversal of the board.

3. Pidbitty during the lesson

4. Rendering home cooking.

Go to lesson.

I AZ

1. Seemingly Russian mathematician and shipbuilder academician Oleksiy Mykolayovich Krilov (1863-1945) once respecting, people turn to mathematics “not in order to be satisfied with good belongings. Yomu persh for everything you need to know about the capital of viprobuvanny instruments and read them correctly and misteriously volodyti. " With one of these tools I have known you - the price is lost. Today at the lesson we are promoting the topic "Pochіdna" and our staff will display the new food "Pochіdna folding function", so it’s just that it’s foldable function and how to count it out.

2. Now let’s guess, how to count the stolen new functions... For all the guilt of the Viconati 7 zavdan. Prior to skin care, the variants of the views are encoded in letters. The correct solution to the skin care allows you to see the need for the letter of the name", F" (x).

Know the lost function.

1) y = 5 y "= 0 Л

Y "= 5x N

Y "= 1 B

2) y = -x y "= 1 V

Y "= -1 A

Y "= x 2 І

3) y = 2x + 3 y "= 3 Y

Y "= x І

Y "= 2 G

4) y = - 12 y "= P

Y "= 1 T

Y "= -12 G

5) y = x 4 y "= П

Y "= 4x 3 A

y "= x 3 З

6) y = -5x 3 y "= -15x 2 N

Y "= -5x 2 Pro

y "= 5x 2 Р

7) y = x-x 3 y "= 1-x 2 D

Y "= 1-3x 2 W

Y "= x-3x 2 A

(Zavdannya on slides 2 - 3).

Otzhe, the nickname of Lagrange, and we ourselves repeated the calculation of the old functions.

3. One of the entries will remember the table: (slide 4).

f (x)	f (1)	f "(x)	f "(1)
1) 4-x
2) 2x 5		10x 4


5) (4-x) 5

Yaki є food? As a result of the conversation, we come to a meeting, but it is not known how to count () "; ((4-x) 3)"

4. Yak is called the function 1), 2), 3), 4).

1) - line, 2) state, 3) state, 4) -?, 5) -?

Infected by me z'yasuєmo, as such functions are called, as numbered from the origin.

II. FNZ і SD.

1. In order to be able to see the function Z = f (x) =

How long does it take to calculate the value of the function?

A) g = 4-x

B) h =

What is the name of the fallowness mіzh g і h?

function

Meaning g and h can be represented in the viewer:

G = g (x) = 4-x

H = h (g) =

As a result of the last display of functions g and h, according to a given value x, the value of any function will be calculated?

F (x)

Z = f (x) = h (g) = h (g (x))

Thus, f (x) = h (g (x)).

It seems that f є is a folding function, folded from g і h. function

g - internal, h - external.

Our butt has 4 internal functions, and √ is called.

G (x) = 4-x

H (g) =

2. Are the offensive functions foldable? For one folding function, name the internal and external (on slide 8, the following functions are written:

a) f (x) = 5x + 1; b) f (x) = (3-5x) 5; c) f (x) = cos3x.

3. Otzhe, mi z'yasuvali, also a folding function. How will I vvazat її I go?

Algorithm for calculating the common folding function f (x) = h (g (x)).

by intrinsic function g (x).
know I will go to the internal function g "(x)
the value of the new function h (g)
know the name of the function h "(g)
to know the tvir of the old internal function for the old internal function g "(x) ∙ h" (g)

Skin memory is given with an algorithm.

4. Doshi teacher: f (x) = (3-5x) 5

g (x) = 3-5x
g "(x) = -5
h (g) = g 5
h "(g) = 5g 4
f "(x) = g" (x) ∙ h "(g) = -5 ∙ 5g 4 = -5 ∙ 5 (3-5x) 4 = -25 (3-5x) 4

5. Otzhe, mi z'yasuvali, so also a folding function and how to count and inherit.

III. Fun.

1. Now let's learn more about the older folding functions. Viconuatsya to the scholars with a slip of the rіvnem to the new.

Know the lost function f (x) =

1) g (x) = 4-x

2) g "(x) = -1

3) h (g) =

4) h "(g) =

5) f "(x) = g" (x) ∙ h "(g) = -1 ∙ = -

2. Know the lost function:

"3" f (x) = (1 - 2x) 4

"4" f (x) = (x 2 - 6x + 5) 7

"5" f (x) = - (1 - x) 3

3. Pidbitty pidsumkiv.

4. D / Z: vivchit algorithm. Know I will disappear.

"3" - f (x) = (2 + 4x) 9

"4" - f (x) =

"5" - f (x) =

Vikoristovuvan literature:

1. Kolmogorov A.N. Algebra and cobs analysis. Pidruchnik for 10 - 11 grades - M .: Education, 2010 rock.

2. Ivlєv B.M., Sahakyan S.M. Didactic materials from algebra and analysis for 10 grades. M .: Education - 2006.

3. Dorofev G.V. "Zbіrnik zavdan for conducting a written education in mathematics for the course middle school"- M.: Bustard, 2007.

4. Bashmakov M.І. Algebra and cobs analysis. Pidruchnik for 10 - 11 grades 2nd ed. - M .: 1992.- 351s.

Lesson number 19Date:

TOPIC: Possibility of folding function

Meta lesson:

coverage:

the formulation of the understanding of the folding function;

the form of vminnya is known for the rule of lost folding function;

inferring to the algorithm of storing the rules of knowing the obsolete folding function in case of new buildings.

developing:

development of vminnya uzagalnyuvati, systematizing on the basis of porvnyannya, robiti visnovok;

to develop naochno-divine creative uyavu;

development of educational interest.

Accept the form in a rational manner, accurately draw up the designation on the documents and in the zoshiti.

Vikhovna:

vikhovuvati of the former prior to the beginning, the will and the ease to achieve the end results with the familiar old folding functions;

take a friendly patronage between the scholars for an hour during the lesson.

Come to blame the nobility:

rules and formulas of differentiation;

the understanding of the folding function;

the rule of knowing the poorest folding function.

To be found guilty of:

count the old folding functions, the vicorist table of the old ones and the rules of differentiation;

zastosovuvati otrimanі knowledge to the finalization of tasks.

Lesson type : reflection lesson.

Bezbechennya lesson:

presentation; table of old; table Differentiation rules;

cards - a factory for individual robots; cards are a tool for converting robots.

ustatkuvannya :

computer, televizor.

HID LESSON:

1. organizational moment(1 xv).

entry

Ready for the class to be robotic.

Zagalny mood.

2. Motivational stage (2-3 min).

(It will be shown by ourselves, that we are ready to meet the knowledge, as we can do things in good times!)

Tell me, did you see your homework for a lesson? (At the last level of the book, a material was given on the topic "Pochidna folding function" and the result of a summary).

Yakim dzherelami did you reprimand when given by those? (Vіdeofіlm, pіdruchnik, supplementary literature).

Yaky pre-dodatkovyuyu literature you skidded? (Literature from the library).

In this rank, the topic of the lesson є ...? ("Good folding function")

It is clear and writeable: a number, the class of the robot, and the topic of the lesson. (Slide 1)

Come along with those, let’s meaningfully intend and learn a lesson (the formulation of the understanding of the folding function, the formulation of the foldable function is also behind the rule of the lost folding function; introduce the algorithm for storing the rule of knowing the stolen folding function)

3. Actualization of knowledge and health of the first child (7-8 min)

Proceed without interruption before reaching the goal of the lesson.

Formulated by the understanding of the folding function (function of the kind y = f ( g (X)) be called folding function, Folded with functions fі g, de f- call of function and g- internal) (slide 2 )

Clear Zavdannya 1: Know the lost function y = (x 2 + sinx) 3 (Record on doshtsі)

Qia function є elementary or folding? (Foldable)

To what? (To this, the argument is not independent of the change x, but the function of x 2 + sinx of the change).

For the knowledge of the obsolete given function, it is necessary to know the basic formulas of the obsolete elementary functions and the knowledge of the rules of differentiation. Zgadaimo oh, having done dictation: (Slide 3)

1) З '= 0; 2) (x n) '= nx n-1; ; 4) a x = a x ln a; 5)

The result of the dictation is overturned (Slide 4)

Vibrate from the tables of old and differentiation rules, which are required for the update given zavdannya and it can be written down in the viglyadi diagrams on the board.

4. Evolution of individual difficulties in the implementation of new knowledge and memory (4 mins)

Virishimo butt 1 and we know the function y '= ( ( x 2 + sin x) 3) '

What are the formulas required for the revision of the plant? ((X n) '= nx n -1;

Robot bіlya boards:

( x 2 + sin x) 3 = U;

y '= (U 3)' = 3 U 2 U` = 3 ( x 2 + sin x) 2 ( 2x + cos x)

You can take a note, but without knowing the formulas and rules it is unwise to take the lost folding function, but for the correct design you need to base it in the differentiation of the main function.

5. Inspiring the plan for the finalization of the difficult and the first implementation (8 - 9 min)

Having found the difficult ones, let's get the algorithm for the knowledgeable folding functions: (Slide 5)

algorithm:

1. Visibility of the call internal functions;

2. It is known in the course of reading the function.

And now we pick it up on the butt

zavdannya 2: Know the lost function:

When forgiven, we will recognize: (5-4x) = U,

y '= ’ =

zavdannya 3: Know the lost function:

1.Viznachamo call and internal functions:

y = 4 U - showing function

2. It is known that I will go along the way of reading the function:

6. Uzagalnennya vyavlennyh difficult (4 min)

N.I. Lobachevsky "... there is no economic region in mathematics, as if it were not possible to fall back on the stagnant state of affairs ..."

To that, our knowledge is worthwhile, the decision of the offensive development is associated with the sound of physical manifestations (bilya doshka for bazhannyam)

zavdannya 4:

In case of electromagnetical connections, which appear in the colival circuit, the charge on the capacitor plates changes according to the law q = q 0 cos ωt, where q 0 is the amplitude of the charge on the capacitor. To know mittєve the meaning of the power of the wicked strum I.

'= -. If you add the cob phase, then the formulas given are mo - .

7. Development of independent robots (6 min)

Scientists check out the test for individual cards in zoshity. One type is not enough, but it’s just a solution. (Slide 6)

Cards "Self-styling of the robot before lesson number 19"

Assessment criteria : "3 vidpovidі" - 3 bali; "2 vidpovidі" - 2 bali; "1 answer" - 1 point

key messages(Slide 7)

№ zavdannya	1 option	2 option	3 option	4 option
№ zavdannya	vidpovid	vidpovid	vidpovid	vidpovid

Pislya reversal (Slide 8)

8. Implementation of the plan with the success of the winners of difficulties (6 - 7 min)

Suggestions for the nutrition of the scientists on the expedited date, as well as in the course of the independent robotics, negotiation typical pardons.

Attach - staff for the news on the winery of the food ***:

9. Home zavdannya(2 xv) (Slide 9)

Visibility and individualization of the cards

Vistavlyannya of evaluations for pods of robots.

10. Reflexion (2 minutes)

"I want to supply"

The scholar asks the food, repairing from the words "I want to supply ...". On the disclaimer, you will see your own emoticon: "I am pleased ...." for "I am not satisfied, so ...".

For the answers of the scholars, bring the bags, which were taken at the time, who reached the end of the lesson.

Theme: "Pohidnafolding function”.

Lesson type: - a lesson in vivchennya new material.

form lesson : Stagnation of information technologies.

Easy lesson in the system of lessons from the given section: first lesson.

tsіlі:

Find out the folding functions, and set the rules for calculating the older ones; udoskonalyuvati subjects, including counting, minus and navichki; Navichki robots with a computer;

development of readiness for informational and initial activity through the provision of information technologies.

wihovuvati adaptability to modern minds.

ustatkuvannya: electronic files with hand-held material, individual computers.

Go to lesson.

I. Organizational moment (1 min.).

II. Setting goals. Motivation of scholars (1 min.).

Primary goals: it is possible to discover the folding functions, the nobility of the rule of differentiation, to set the formula for the obsolete folding function in the case of new buildings; udoskonalyuvati subjects, including counting, minus and navichki; Navichki robots with a computer.

Developing goals: developing educational interests through information technologies.

Vyhovnі tsіlі: wihovuvati adaptability to modern minds.

III. Actualization of basic knowledge (5 min.).

Name the rules for calculating the lost.

3. Sleep of the robot.

Know the lost functions.

a) y = 2x 2 + XI;

b) f (x) = 3x 2 - 7x + 5;

c) f (x) =;

d) f (x) = 1 / 2x 2 ;

e) f (x) = (2x - 5) (x + 3).

4. Rules for calculating lost .

Repetition of formulas on a computer with a sound superwire.

IV. Programming control (5 min.).

Know I will disappear.

Be aware of more zoshits. In diagnostic maps, indicate the default with the + sign, and not the default with the "-" sign.

V. Vivchennya new material (5 min.).

folding function.

The function is easy to see, given by the formula f (x) =

In order to know the lost function, you need to count the lost internal function.u = v (x) = XІ + 7x + 5, and then calculate the lost functiong (u) = .

Seems like the functionf (x) - є foldable function, folded with functionsg іv , I write:

f (x) = g (v (x)) .

The area of \ u200b \ u200bthe folding function - without all the quietNS in the area of assigned functionsv , for thosev (x) enter the scope of the assigned functiong.

THEOREM.

Let the folding function y = f (x) = g (v (x)) be such that the function y = v (x) is assigned to the interval U, and the function u = v (x) is assigned to the interval X; in the middle of U. Let the function u = v (x) go to the skin point in the middle of the X, and the function y = g (u) go to the skin point in the middle in U. The same function y = f (x) in the middle the points in the middle of the X, which are calculated according to the formula

y " x = Y " u u " x .

The formula is read like this: losty onx darlingy onu , Multiplied by the lostu onx .

The formula is written like this:

f "(x) = g" (u) v "(x).

Delivered.

At pointNS NS given a priority to an argument, (X +NS)NS. Todi functionu = v (x) gain a gain , and the functiony = g (u) gain a gain y. Treba vrahuvati, scho, so yak functionu = v (x) in pointx I’m going to go, then she’s not interrupted at the point andat . y = (1 + x 2 ) 100 .

Decision.

Buttstock 2 і buttstock 3 from the handler

Rishennya attachments № 304, № 305, № 306 with a further change on the computer.

Vii. butt for independent solution(8 minutes).

On the working table of the computer. 5(P - x);

y = sin (2x 2 – 3).

y = (1 + sin3x) cos3x;

y = tg x (tg x - 1).

IX. A lesson bag (1 min.).

Date of registration of funky functions.

Name the rules for calculating the old.

Is the function foldable?

What is the area of the folding function?

Name the formula for the meaningful folding function.

X. Home office (0.5 min.).

§4. P16. No. 224. Individual records on cards.

DISCIPLINE ELEMENTS OF VISCHO MATHEMATICS FOR SPECIAL PROGRAMS SAFE COMPUTER TECHNIQUES AND AUTOMATED SYSTEMS

PLAN TO EMPLOY

1 ORGANIZATION MOMENT

1.1 Intro

1.2 Preparedness of a group for a robot

1.3 Setting a busy day

2 REPEATED MATERIALU

2.1 Frontal experience

2.2 The individual robot behind the cards

2.3 Gra "Domino"

2.4 Robot Sleep

3 EXPLANATION OF THE NEW MATERIAL

3.1 Suitable for folding function

4 STAYED KNOWLEDGE AT VIRISHENNY TYPICAL ZAVDAN

5.1 Reverse robot with vibrating display system

6 lines

6.1 Delivery of pidsumkiv

6.2 Homework

TOPIC: FOLDING FUNCTIONS

Employment type: combinations

Tsіlі vivchennya by those:

coverage:

the formulation of the understanding of the folding function;
the form of vminnya is known for the rule of lost folding function;
inferring to the algorithm of storing the rules of knowing the obscure folding function in case of virtual attachments.

developing:

development of vminnya uzagalnyuvati, systematizing on the basis of porvnyannya, robiti visnovok;
to develop naochno-divine creative uyavu;
development of educational interest.

Vikhovna:

vykhovannya vіdpovіdalnoy put before the beginning of pratsі, will and easeliness for achieving endurance results with the familiar old folding functions;
the formulation is rational;
vikhovannya amicable presentation between students during the lesson.

Zabpechennya busy:

table of old;
table Differentiation rules;
cards for gris domino;
cards - a factory for individual robots;
cards are a tool for converting robots.

The student is guilty of the nobility:

viznachennya obh_dnoyu;
rules and formulas of differentiation;
the understanding of the folding function;
the rule of knowing the poorest folding function.

The student is guilty of:

count the old folding functions, the vicorist table of the old ones and the rules of differentiation;
zastosovuvati otrimanі knowledge to the finalization of tasks.

XID ZANYATTYA

I ORGANIZATION MOMENT

entry
Group ready to robot
Setting up a busy day

II PERSONALIZATION OF THE HOME

a) Nutrition for frontal support:

How to be called a rude function at a point?
. What kind of differentiation?
Is the function called differentiation in points?
What does it mean to calculate the cost of the algorithm?
Do you know the rules of differentiation?
How is the interconnection of the function without interruption at the point and the differentiability at the point?

b) individual robot behind cards

c) Gra "Domino"

NS /		() /
Z /		() /
() /		f / (x)
() /		() /
() /
() /		() /
() /		() /
() /		() /
() /		() /
() /	2 x	() /

The set "Domino" has 20 cards. Bet to change your cards, move around and fix the placement of dominoes from cards, in which only the right and left part are stored. We are guilty of knowing on the first card the viraz can also be violated on the first card and so on. As a result, go lance.

We will predominantly apply only todies, if all the cards of the victorian and the extreme halves of the last and first cards are empty.

It’s not all the cards that have been laid out, so it’s like they’ve made a pardon, and it’s necessary to know.

Students who work in guilt to rate one one and list the assessments in the control sheet. Evaluation criteria for writing on envelopes.

Assessment criteria:

"5" - no pardons;
"4" - 1-2 pardons;
"3" - 3-4 pardons.

d) Sleep of the robot

butt 1 Know the lost function.

Solution:.

butt 2 Know the lost function.

Solution:.

butt 3 Know the lost function.

Solution:.

butt 4 Statement of a problem situation: know the lost function

y = ln (cos x).

Mi maєmo here logarithmic function, The argument is that there is no square to serveх, and the function cos x a lot of snazzy.

Yak called this kind of function?

[This kind of function is called folding

Functions and functions of functions.]

Do I know old folding functions?

[Ні.]

So, why do we know at once?

[For the familiar foldable functions.]

How will the theme of our current busyness be heard?

[Easy folding function]

Students themselves formulate the topic and mark the lesson, the weekend will write down the topic in the school, and the students - in the school.

III VIVCHENNYA NEW MATERIALU

The rules and formulas of differentiation, which we looked at last busy, are the main ones when calculating old ones.

However, if for awkward virazs, the basic rules do not become special difficulties, then for folding virazs, balkan rules you can see the right velma copy.

The meta of our current busyness is to look at the understanding of the folding function and the technology of differentiation of the folding function, so that the technology of storing basic formulas in the differentiation of folding functions.

Suitable for folding function

From the butt, you can see that the folding function is the function of the function. Also, it is possible to date the folding function:

Meaning: Function type

y = f (g (x))

be called folding function, Folded with functions f u g, abo superposition of functions f і g.

Application: Functions y = ln (cos x) є foldable function, foldable with functions

у = ln u і u = cos x.

This folding function is often written at the viglyad.

y = f (u), de u = g (x).

The name of the function of the Industrial

function

With tsom argument x name Independent Change of Noah, And u - intermediate argument.

Let's turn to the butt... I will go dermal from the cich functions and can count the vicorist table of the older ones.

How can I count the folding functions?

On the basis of the supply, the theorem is on.

Theorem: The function u = g (x) differentiated in deyak_y point x 0, and the function y = f (u) differentiated in points u 0 = g (x 0 ), Then a folding function y = f (g (x)) differentiated in tsy point x 0 .

With tsom

abo

to go from y by zminniy x road to old for change i , Multiplied by lost from and according to the change.

rule:

To know the folding function, you need to read it correctly;
To correctly read the function, you need to put it in the right order;
Reading function in vortex order go straight;
I will go familiar in the course of reading the function.

And now we pick it up on the butt:

Application 1: Functions y = ln (cos x) to go to the last vikonannya two operations: taking the cosine kut NS і value of the total number of the natural logarithm:

The function is read like this: logarithmic function as trigonometric function.

Let's differentiate the function: y = ln (cos x) = ln u, u = cos x.

At the practical time, differentiation is carried out on a shorter and simpler basis, at any time, without the introduction of a recordі.

The mastery of differentiation of the folding function of the field in the smarter backyard at the time of differentiation of only one function (the same is differentiated in the Danish moment), without the need to leave it, until the moment of determination.

We will be victorious when differentiating an additional table of the older ones.

Butt 2: Know the lost function y = (x 3 - 5x + 7) 9.

Decision : Having defined in "umi" u \ u003d x 3 - 5x +7, we can take mo y \ u003d u 9. we know:

For the formula maєmo

4 STAYED KNOWLEDGE AT VIRISHENNY TYPICAL ZAVDAN

1) ;

2) ;

3) ;

4) ;

5) ;

5 SELF STICKED KNOWLEDGE, MIND AND NAVICHOK

5.1 Reconstruction of the robot in the test form

Specification of the test:

The test is homogeneous;
Close form test;
Number of buildings - 3;
Visiting hour of the day - 5khv.;
For the correct display of vip tests I will take out 1 point,

For wrong - 0 points.

Instructions: choose the correct display option.

Assessment criteria:

"5" - 3 bali

"4" - 2 bali

"3" - 1 point

Students look on the sheets of paper and change the view for an additional key presented on the board. Put the assessment in the control sheet (self-control).

Option 1

Possible functions of the road:

a); b); v).

Possible functions of the road:

a); b); v).

Option 2

Viber is the correct version of the message

Possible functions of the road:

a); b); v).

Possible functions of the road:

a); b); v).

Calculate lost for the function:

a); b); v).

option 3

Viber is the correct version of the message

Possible functions of the road:

a); b); v).

Possible functions of the road:

a); b); v).

Calculate lost for the function:

a); b); v).

option 4

Viber is the correct version of the message

Possible functions of the road:

a); b); v).

Possible functions of the road:

a); b); v).

Calculate lost for the function:

a); b); v).

key messages

Registration number	1 option	2 option	3variant	4 option
	vidpovid	vidpovid	vidpovid	vidpovid