AP Calculus BC Tuesday, 22 September 2015 OBJECTIVE TSW apply the Chain Rule to differentiate...
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![Page 1: AP Calculus BC Tuesday, 22 September 2015 OBJECTIVE TSW apply the Chain Rule to differentiate functions. ASSIGNMENT DUE TOMORROW/THURSDAY –Sec. 3.4: pp.](https://reader036.fdocuments.in/reader036/viewer/2022062805/5697bfa91a28abf838c99be0/html5/thumbnails/1.jpg)
AP Calculus BCTuesday, 22 September 2015
• OBJECTIVE TSW apply the Chain Rule to differentiate functions.
• ASSIGNMENT DUE TOMORROW/THURSDAY– Sec. 3.4: pp. 170-171 (7, 8, 11, 12, 15-19
odd, 20, 25, 26, 40. 41)– Sec. 3.3: p. 161 (44, 45, 47)
• TODAY’S ASSIGNMENT (due Friday, 09/25/15)
– Sec. 3.7: pp. 198-199 (7-10 all, 19-33 odd (omit 27), 57, 61, 65)
![Page 2: AP Calculus BC Tuesday, 22 September 2015 OBJECTIVE TSW apply the Chain Rule to differentiate functions. ASSIGNMENT DUE TOMORROW/THURSDAY –Sec. 3.4: pp.](https://reader036.fdocuments.in/reader036/viewer/2022062805/5697bfa91a28abf838c99be0/html5/thumbnails/2.jpg)
Sec. 3.7: The Chain Rule
![Page 3: AP Calculus BC Tuesday, 22 September 2015 OBJECTIVE TSW apply the Chain Rule to differentiate functions. ASSIGNMENT DUE TOMORROW/THURSDAY –Sec. 3.4: pp.](https://reader036.fdocuments.in/reader036/viewer/2022062805/5697bfa91a28abf838c99be0/html5/thumbnails/3.jpg)
Sec. 3.7: The Chain Rule Easy to differentiate:
Not easy to differentiate:
Easy to differentiate:
Not easy to differentiate:
Easy to differentiate:
Not easy to differentiate:
3 4y x
233 4y x
cosf x x
cos7f x x
9 7g x x
9 7g x x
![Page 4: AP Calculus BC Tuesday, 22 September 2015 OBJECTIVE TSW apply the Chain Rule to differentiate functions. ASSIGNMENT DUE TOMORROW/THURSDAY –Sec. 3.4: pp.](https://reader036.fdocuments.in/reader036/viewer/2022062805/5697bfa91a28abf838c99be0/html5/thumbnails/4.jpg)
Sec. 3.7: The Chain Rule
How does one item change with respect to another?
Ex: There are 3 gears, labeled #1, #2, and #3. Gear one is the smallest, followed by gear two, and finally gear three.
#1 rotates four times as fast as #2. #2 rotates five times as fast as #3.
How much faster is #1 rotating than #3?
(4)(5) = 20 times as fast
This demonstrates the CHAIN RULE.
![Page 5: AP Calculus BC Tuesday, 22 September 2015 OBJECTIVE TSW apply the Chain Rule to differentiate functions. ASSIGNMENT DUE TOMORROW/THURSDAY –Sec. 3.4: pp.](https://reader036.fdocuments.in/reader036/viewer/2022062805/5697bfa91a28abf838c99be0/html5/thumbnails/5.jpg)
Sec. 3.7: The Chain Rule
The Chain Rule
![Page 6: AP Calculus BC Tuesday, 22 September 2015 OBJECTIVE TSW apply the Chain Rule to differentiate functions. ASSIGNMENT DUE TOMORROW/THURSDAY –Sec. 3.4: pp.](https://reader036.fdocuments.in/reader036/viewer/2022062805/5697bfa91a28abf838c99be0/html5/thumbnails/6.jpg)
Sec. 3.7: The Chain Rule Ex: Differentiate:
121a) f x x
23b) 2f x x
111 112f x x 11
12 1x
1 223 2x
1 221
3 22
6xf x x
2
3
3 2
x
x
![Page 7: AP Calculus BC Tuesday, 22 September 2015 OBJECTIVE TSW apply the Chain Rule to differentiate functions. ASSIGNMENT DUE TOMORROW/THURSDAY –Sec. 3.4: pp.](https://reader036.fdocuments.in/reader036/viewer/2022062805/5697bfa91a28abf838c99be0/html5/thumbnails/7.jpg)
Sec. 3.7: The Chain Rule
The General Power Rule
![Page 8: AP Calculus BC Tuesday, 22 September 2015 OBJECTIVE TSW apply the Chain Rule to differentiate functions. ASSIGNMENT DUE TOMORROW/THURSDAY –Sec. 3.4: pp.](https://reader036.fdocuments.in/reader036/viewer/2022062805/5697bfa91a28abf838c99be0/html5/thumbnails/8.jpg)
Sec. 3.7: The Chain Rule Ex: Differentiate:
1a)
3 1f x
x
13 1x
21 3 1 3f x x
23
3 1x
![Page 9: AP Calculus BC Tuesday, 22 September 2015 OBJECTIVE TSW apply the Chain Rule to differentiate functions. ASSIGNMENT DUE TOMORROW/THURSDAY –Sec. 3.4: pp.](https://reader036.fdocuments.in/reader036/viewer/2022062805/5697bfa91a28abf838c99be0/html5/thumbnails/9.jpg)
Sec. 3.7: The Chain Rule Ex: Differentiate:
cos 3b) y x
sin 33y x
3 sin 3 x
![Page 10: AP Calculus BC Tuesday, 22 September 2015 OBJECTIVE TSW apply the Chain Rule to differentiate functions. ASSIGNMENT DUE TOMORROW/THURSDAY –Sec. 3.4: pp.](https://reader036.fdocuments.in/reader036/viewer/2022062805/5697bfa91a28abf838c99be0/html5/thumbnails/10.jpg)
Sec. 3.7: The Chain Rule Ex: Differentiate:
2c tc) oy x 2cot x
22 c csot cy x x
22cot cscx x
![Page 11: AP Calculus BC Tuesday, 22 September 2015 OBJECTIVE TSW apply the Chain Rule to differentiate functions. ASSIGNMENT DUE TOMORROW/THURSDAY –Sec. 3.4: pp.](https://reader036.fdocuments.in/reader036/viewer/2022062805/5697bfa91a28abf838c99be0/html5/thumbnails/11.jpg)
Sec. 3.7: The Chain Rule Ex: Find all points on the graph of
223 1f x x for which 0 andf x
DNE.f x
2 32 1f x x
1 32 1 2
2
3f x x x
3 2
4
3 1
x
x
![Page 12: AP Calculus BC Tuesday, 22 September 2015 OBJECTIVE TSW apply the Chain Rule to differentiate functions. ASSIGNMENT DUE TOMORROW/THURSDAY –Sec. 3.4: pp.](https://reader036.fdocuments.in/reader036/viewer/2022062805/5697bfa91a28abf838c99be0/html5/thumbnails/12.jpg)
Sec. 3.7: The Chain Rule Ex: Find all points on the graph of
223 1f x x for which 0 andf x
DNE.f x
3 2
4
3 1
xf x
x
0 :f x 4 0x 0x 0,1
DNE :f x 3 23 1 0x 1x 1, 0 , 1, 0
![Page 13: AP Calculus BC Tuesday, 22 September 2015 OBJECTIVE TSW apply the Chain Rule to differentiate functions. ASSIGNMENT DUE TOMORROW/THURSDAY –Sec. 3.4: pp.](https://reader036.fdocuments.in/reader036/viewer/2022062805/5697bfa91a28abf838c99be0/html5/thumbnails/13.jpg)
Sec. 3.7: The Chain Rule Ex: Differentiate:
s) n4a iy x
2cos 3b) 2f x x
cos4 4xy 4cos4x
2sin 3 62x xf x
26 sin 3 2x x
![Page 14: AP Calculus BC Tuesday, 22 September 2015 OBJECTIVE TSW apply the Chain Rule to differentiate functions. ASSIGNMENT DUE TOMORROW/THURSDAY –Sec. 3.4: pp.](https://reader036.fdocuments.in/reader036/viewer/2022062805/5697bfa91a28abf838c99be0/html5/thumbnails/14.jpg)
Sec. 3.7: The Chain Rule Ex: Differentiate:
3t nc) ay x
3tand) g x x
3tan x
2 3 2sec 3y x x 2 2 33 secx x
3tanx
2 23 tan secg xx x 2 23 tan secx x
![Page 15: AP Calculus BC Tuesday, 22 September 2015 OBJECTIVE TSW apply the Chain Rule to differentiate functions. ASSIGNMENT DUE TOMORROW/THURSDAY –Sec. 3.4: pp.](https://reader036.fdocuments.in/reader036/viewer/2022062805/5697bfa91a28abf838c99be0/html5/thumbnails/15.jpg)
Sec. 3.7: The Chain Rule Ex: Differentiate:
2 3coe) s 4y x 23cos 4x
3 3 212si2 cos 44 n xxy x Double - angle for sine :
2sin cos sin2 2 3 32sin o2 4 s 41 cx xx
2 312 sin 8x x
2 312 sin 8x x
![Page 16: AP Calculus BC Tuesday, 22 September 2015 OBJECTIVE TSW apply the Chain Rule to differentiate functions. ASSIGNMENT DUE TOMORROW/THURSDAY –Sec. 3.4: pp.](https://reader036.fdocuments.in/reader036/viewer/2022062805/5697bfa91a28abf838c99be0/html5/thumbnails/16.jpg)
Sec. 3.7: The Chain Rule Ex: Differentiate:
3 22a) f x x x 1 23 22x x
1 2 1 23 2 2 2122 2 3
2f x x xx x x
1 2 1 24 2 2 22 3 2x x x x
1 2 12 2 2 22 3 2x x x x
2 2 2
1 22
6 3
2
x x x
x
2 2
1 22
4 6
2
x x
x
2 2
2
2 2 3
2
x x
x
![Page 17: AP Calculus BC Tuesday, 22 September 2015 OBJECTIVE TSW apply the Chain Rule to differentiate functions. ASSIGNMENT DUE TOMORROW/THURSDAY –Sec. 3.4: pp.](https://reader036.fdocuments.in/reader036/viewer/2022062805/5697bfa91a28abf838c99be0/html5/thumbnails/17.jpg)
Sec. 3.7: The Chain Rule Ex: Differentiate:
3 2
b)4
xf x
x
1 32 4
x
x
1 3 2 32 2
21 32
14 1 4
32
4
x x xf x
x
x
2 3 12 2 2
2 32
24 4
3
4
x x x
x
2
4 32
14
3
4
x
x
2
4 32
12
3 4
x
x
3
3
![Page 18: AP Calculus BC Tuesday, 22 September 2015 OBJECTIVE TSW apply the Chain Rule to differentiate functions. ASSIGNMENT DUE TOMORROW/THURSDAY –Sec. 3.4: pp.](https://reader036.fdocuments.in/reader036/viewer/2022062805/5697bfa91a28abf838c99be0/html5/thumbnails/18.jpg)
Sec. 3.7: The Chain Rule Ex: Differentiate:
3
2c)
2 1
4
xy
x
2 22
2 2 4 22 13
4
2 1 2
4
x x x
x
xy
x
2 22
2 22
2 8 4 22 13
4 4
x x xx
x x
2 2
2 22
2 1 2 2 83
4 4
x x x
x x
22
2 22
2 42 13
4 4
x xx
x x
2 2
42
6 2 1 4
4
x x x
x
![Page 19: AP Calculus BC Tuesday, 22 September 2015 OBJECTIVE TSW apply the Chain Rule to differentiate functions. ASSIGNMENT DUE TOMORROW/THURSDAY –Sec. 3.4: pp.](https://reader036.fdocuments.in/reader036/viewer/2022062805/5697bfa91a28abf838c99be0/html5/thumbnails/19.jpg)
Sec. 3.7: The Chain Rule
Summary of Differentiation Rules
![Page 20: AP Calculus BC Tuesday, 22 September 2015 OBJECTIVE TSW apply the Chain Rule to differentiate functions. ASSIGNMENT DUE TOMORROW/THURSDAY –Sec. 3.4: pp.](https://reader036.fdocuments.in/reader036/viewer/2022062805/5697bfa91a28abf838c99be0/html5/thumbnails/20.jpg)
Sec. 3.7: The Chain Rule PPT Problems (put on a clean sheet of
notebook paper): Due tomorrow/Thursday, 09/23-24/15.
)2
11
f xx
2
2
3
3)
12
xf x
x
2co3) s 3y x 2si 34 n) y x
Find each derivative; simplify your answer.