常见函数的导数PPT课件

4.路灯距地面为8m,一个身高为1.6m的人 以84m/min的速率在地面上行走,从路 灯在地平面上射影点C,沿某直线离开路 灯,求人影长度的变化率.
2020/6/12
pyramid 金字塔
Stonehenge 巨石阵
wheel 车轮
golden sunlight. 金色阳光
army 军队
3、若直线y=3x+1是曲线y=ax3 的切线,试求a的值.
解:设直线y=3x+1与曲线y=ax3相切于点
P(x0,y0),则有:
y0=3x0+1①, y0=ax03②, 3ax02=3.③
由①,②得3x0+1=ax03,由③得ax02=1,代 入上式可得:3x0+1=x0,x0=－1/2.
所以a•(-1/2)2=1, 即:a=4
take bring carry 随身携带
4. They all went to sleep, including the gate guards. The band played many songs, including some of my favorite. 十个人出席了会议，包括我爸爸。
7.进入城里
enter the city= get into city
8. 拿走，带走 take away
9. 除…之外
except for
10.拖…进城
pull / drag… into the city
11.开…玩笑
make jokes about = laugh at= make fun of
3.HWheatpdridotbheacbaplytainwthainsk faebeoulitnthge hsoursre?prised.
The captain thought that they had won the war.
He thought it was too big for the Greeks to take.
公式六:对数函数的导数
(1)
(loga
x)
x
1 ln
a
(a
0,
a
1).
(2) (ln x) 1 . x
例1.求下列函数的导数
(1) y 4x
(2)
y
log
x 3
2020/6/12
1、求下列函数的导数
(1)x sin t (4)u cosv
(2) y 2x
(5) y x 3
(3) y log0.2 x
aptured
1.大木马
a huge wooden horse
2. 举行一次比赛 have\ hold\ run a competition
3. 冲下台阶
rush down the stairs
4.一会儿后
seconds later
5.朝下看
look down at
6. 再多等一小时 wait for another hour=wait for one more hour
Read the passage and then answer the following questions
1.How was the soldier probably feeling when he came down the stairs, surprised or peaceful? 2. What did the captain think when he saw the empty plain?
12.成功做成某事 succeed in doing sth.
13. 用计谋
with a trick
Useful expressions
1.A newspaper ran a short competition on famous tales from history.
compete (v)比赛---- competition competitor competitive
1:求过曲线y=cosx上点P( , 1 )
的切线的直线方程.
32
解： f (x) cosx, f (x) sin x,
f ( ) sin 3 .
3
32
故曲线在点 P( , 1 )处的切线斜率为 3 ，
32
2
所求的直线方程为 y 1 3 (x ),
22 3
即 3x 2 y 1 3 0.
(n.)比赛 (n.)比赛者 (adj.) 比赛的
2. Seconds later, the captain stood on the high wall of the city of Troy, and looked down at the empty plain.
(1) seconds later = after a while 一会儿后(几秒钟后) (2) the city of Troy 特洛伊城
荷马
the prince of Troy fell in love with Helen, the queen of
Sparta.
斯巴达
绑架 He kidnapped her and took her to Troy. All the Greek
went to bring her back.
the war lasted for ten years.
4.What did the citizens of Troy do that night?
They celebrated their success.
5.Where did the six Greek soldiers hide ?
They hid in the horse.
6. Did the horse have something to do with the trick? How?
Tian’anmen Square 天安门广场
Jay Chou 周杰伦
Jay Chou is handsome. He is my favourite actor.
arrow 箭 bow 弓
The Trojan War
the Trojan War told in Homer’s
I伊lia利d 亚特and Odyssey． 奥德赛
3. What did the captain think about the horse?
4.What did the citizens of Troy do that night?
5.Where did the six Greek soldiers hide ?
6.Did the horse have something to do with the trick? How?
P3-6
The Greek soldiers inside the horse open the city gates and let in the Greek army. The Greek army capture Troy.
A Trojan soldier announces that the
Summary The war between the Troy and the Greeks lasted ten years. At last, the Greeks won the war with a t___. They pretended to leriackve the city of Troy, but they left a huge w______ horse behind. The Troy thought tohoedyenhave w__ the war so they c________, making j____ abouotnthe Greeks. Theeylebwraetreed so happy about othkeesir win that all of them went to sleep, i________ the gate guard. The Greek soldiers i_____ the wooden horse openncleuddinthge gate and let their army in. In this way, they c_____ thnesidTeroy city.
Yes. (answers vary.)
Part B Look and think
These pictures show some of the events in the story on Page 58. Arrange them in the correct order.
Answers: c d b a f e
Ten members are present at the meeting, including my father. 5. By midnight, the square was empty, except for the giant horse.
(6)
y
1 x2
(7) y 5x5 (8) y 2 (9) y ex (10) y ln x
2、已知f (x) xa ,且f (1) 4,
求实数a.
2020/6/12
注意:关于a x和xa 是两个不同
的函数,例如:
(1)(3x ) 3x ln a
(2)( x3) 3x2
经典例题选讲
the city of Shenzhen=Shenzhen city
(3) look out = be careful look for 寻找 look after 照顾 look over = examine look down upon sb 看不起某人 look up to 看得起，尊重
3.It was too big for them to take with them. =It was so big that they couldn’t take it with them.
3.2.1 常见函数 的导数(2)
一、复习
公式一: C= 0 (C为常数)
公式二:(x ) x 1(是常数)
公式三: (sin x) cos x
公式四: (cos x) sin x
公式五:指数函数的导数
(1) (a x ) a x ln a(a 0, a 1).
(2) (ex ) ex.
3
2:若直线y=4x+b是函数y=x2图象 的切线,求b以及切点坐标.
解 : 设切点P(x0 , y0 ) f (x) (x2 ) 2x 2x0 4, x0 2, y0 22 4 即切点坐标(2,4), 由题意得此点也在直线y 4x b上 4 4 2 b,b 4
练习: P69T4
The night of the horse
ቤተ መጻሕፍቲ ባይዱ
Look at the title, the picture and the last paragraph, and then answer the two questions.
1. What kind of horse it is?
I2t.Howw daidstheaGrheeuksgwien thwe woaro? den horse.
P7
Greek army has left and his captain Confirms it.
P8-9
The soldier found a huge, wooden horse outside their city, and the captain orders it to be moved into the city.
Read the passage and then answer the following questions
1.How was the soldier probably feeling when he came down the stairs, surprised or peaceful?
2. What did the captain think when he saw the empty plain?
They won the war with a trick.
Read through the whole passage and match the main idea for each part.
P1-2
The Trojans celebrate their victory and then go to sleep.