THUYẾT TRÌNH ĐẠO HÀM BẰNG TIẾNG ANH DERIVATIVES

Calculate: tính Form: lập Ratio: tỉ số, tỉ lệCalculate: tính Form: lập Ratio: tỉ số, tỉ lệ 2.. How to calculate a derivative by definition... Calculate the derivative of function at poin

Instructors : … Presentation group 4: ….

5 DERIVATIVE OF

A TRIGONOMETRIC

6 THE SECOND DERIVATIVE

I Definition of a derivative at a

point

1 Definition

 Given function defined on the open

interval (a;b) and

 If there exists (finite) limit

 Then the limit is called a derivative

Calculate: tính Form: lập Ratio: tỉ số, tỉ lệ

Calculate: tính Form: lập Ratio: tỉ số, tỉ lệ

2 How to calculate a derivative by definition

Example 1 Calculate the derivative of function

at point  

Solution: Let be the increment of an argument at We have:

divided by x, we shall show:

Then,

Therefore,

▹  

Example 2 Calculate the derivative of function

at point  

Solution: Let be the increment of an argument at We have:

divided by x, we shall show:

Then,

Therefore,

▹  

8

II Derivativers of some common functions

Theorem 1 : Function has

a derivative at every and

Theorem 2 : Function has a derivative at every

positive x and

Example 1 Find the dervative of function

10

▹ Remax a) Derivative of a constant function equals 0

b) Derivative of function

y = x equals 1

a) b)

Remax: nhận xét

Constant function: hàm hằng

III Derivative of sum, difference, product and quotient

1 Theorem

Theorem 3: Suppose u = u(x) and v = v(x) are functions with

derivatives at point x on the defined interval We have

) 0 )

( (

) (

) (

) (

v v

v u v

u v

u

v u v

u uv

v u

v u

v u

v u

 Quotient: thương

 Suppose: giả sử

 Defined interval: khoảng xác định

1 2 3 4

5 (

x

x x

x x

=

b) We have:

c) We have:

 

2

) 3 (

) 3 )(

2 1 ( ) 3 (

2

1 3

2 1

x x

x

2

2 ( 3 )

7 )

3 (

) 2 1 ( ) 3 (

x x

2

1

v

v v

ku)    (

Example 2: Find the derivative of function

2

) 1 (

8 16

) )(

1 2

( )

1 2

( 1

2

x

x x

x

x x

IV Derivative of a composite function

Theorem 4 If function has derivative at x and function has derivative at , then composite function has a derivative at

▹  

16

x u

x y u

y    

composite function: hàm hợp

Example 1: Find the derivative of function

Example 1: Find the derivative of function

VI THE SECOND DERIVATIVE

1 DEFINITION

20

Assume function has a derivative at every point Then, relation defines a new function on the interval (a;b) If function has another derivative at , then we call the

derivative of function is the second derivative of function at

and denoted by or

▹  

Example 1: Find the second derivative and the

n th derivative of the follwing functions:

GAME RULES

THREE GROUPS WILL PARTICIPATE IN

A THREE - PART GAME:

1 Starting up

 2 Acceleration

3 To the finish line

At the end of the 3 sessions, the team with the highest total

score will win and win a prize.

When one team participates in the game, the other 2 teams will act as judges and the secretary will sum up the points for each group.

RULE:

There are 3 question packs , each with 30

seconds of thinking and answering time Each

score bank If you answer incorrectly , you will receive no points.

At the end of the 3 - pack questioning which group is the highest , that group wins in this

game.

STARTING UP

1 2 3

Select the questionnaire package

STARTING UP

ACCELERATIONACCELERATION

about the group giving the answer, if it is

right to answer will be given to another group.

At the end of the 7 questions, which group is

1 2 3 4

Choose the

ACCELERATION

AWRONG! RIGHT!

D

AWRONG! RIGHT!

D

QUESTION 2

AWRONG! RIGHT!

D

QUESTION 3

Question 4 Find the derivative of function:

AWRONG! RIGHT!

D

QUESTION 4

RIGHT!

D

QUESTION 5

AWRONG!

SING A VIETNAMESE CHIDREN’S SONG AND GET 10 POINTS IN THE SCORE FUND

DEDUCTED 10 POINTS

1 2

TO THE FINISH LINE

TO THE

FINISH LINE

Each team records the vocabulary they learned

in the derivative presentation of group 4 on the prepared paper sample Time for each team is 3 minutes Exactly one word gets one point The team with the most correct words is the winner.

RUL E

THANK

YOU

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