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
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.
(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
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?
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.
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?
The night of the horse
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.
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.
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
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
Ten members are present at the meeting, including my father. 5. By midnight, the square was empty, except for the giant horse.
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
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.
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?
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?
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
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.
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.
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
12.成功做成某事 succeed in doing sth.
13. 用计谋
with a trick