product and quotient rule
DESCRIPTION
Product and Quotient Rule. By: Jenna Neil Lori Hissick And Evan Zimmerman Period 4. Product Rule. Derivative times uv = u times the derivative of v plus derivative of u. Product Rule. Example: U V Y=. Quotient Rule. Lo De Hi – Hi De Lo all over Lo squared - PowerPoint PPT PresentationTRANSCRIPT
![Page 1: Product and Quotient Rule](https://reader035.vdocuments.us/reader035/viewer/2022070419/56815c3e550346895dca3bd7/html5/thumbnails/1.jpg)
Product and Quotient Rule
By: Jenna NeilLori Hissick
And Evan Zimmerman
Period 4
4429 2 xx
![Page 2: Product and Quotient Rule](https://reader035.vdocuments.us/reader035/viewer/2022070419/56815c3e550346895dca3bd7/html5/thumbnails/2.jpg)
Product Rule
• Derivative times uv = u times the derivative of v plus derivative of u
d uv udv vdu( )
![Page 3: Product and Quotient Rule](https://reader035.vdocuments.us/reader035/viewer/2022070419/56815c3e550346895dca3bd7/html5/thumbnails/3.jpg)
Product Rule
• Example: U
VY=
)43)(7( 2 xx
43426 22 xxx
4429 2 xx
)1)(43()6)(7( 21 xxxY
![Page 4: Product and Quotient Rule](https://reader035.vdocuments.us/reader035/viewer/2022070419/56815c3e550346895dca3bd7/html5/thumbnails/4.jpg)
Quotient Rule
• Lo De Hi – Hi De Lo all over Lo squared • U = numerator • V = denominator
vdu udvv2d u
v( )
![Page 5: Product and Quotient Rule](https://reader035.vdocuments.us/reader035/viewer/2022070419/56815c3e550346895dca3bd7/html5/thumbnails/5.jpg)
Quotient Rule• Example:
*Leave the bottom the way it is!*
2 53
3
2
x xx
22
322
)3()2)(52()56)(3(
x
xxxxx
22
24
)3(15132
x
xx
![Page 6: Product and Quotient Rule](https://reader035.vdocuments.us/reader035/viewer/2022070419/56815c3e550346895dca3bd7/html5/thumbnails/6.jpg)
And the game’s begin…
yx
63
#1)
#1 Answer) yx x
12
66 9
![Page 7: Product and Quotient Rule](https://reader035.vdocuments.us/reader035/viewer/2022070419/56815c3e550346895dca3bd7/html5/thumbnails/7.jpg)
• #2)
yx
x x
4
2sincos
#2 Answer)
Yx x x
x x1
2
8 42
( co s sin )( co s )
![Page 8: Product and Quotient Rule](https://reader035.vdocuments.us/reader035/viewer/2022070419/56815c3e550346895dca3bd7/html5/thumbnails/8.jpg)
• #3)
Yxx
2
3 1#3 Answer)
)13(51
x
Y
![Page 9: Product and Quotient Rule](https://reader035.vdocuments.us/reader035/viewer/2022070419/56815c3e550346895dca3bd7/html5/thumbnails/9.jpg)
• #4)
Yxx
20 4
8
#4 Answer)
Yx
12
1648
( )
![Page 10: Product and Quotient Rule](https://reader035.vdocuments.us/reader035/viewer/2022070419/56815c3e550346895dca3bd7/html5/thumbnails/10.jpg)
• #5)
Yx
37 6204
,
#5 Answer)
Yx
12
37 6204
,
( )
![Page 11: Product and Quotient Rule](https://reader035.vdocuments.us/reader035/viewer/2022070419/56815c3e550346895dca3bd7/html5/thumbnails/11.jpg)
• #6)
Y x x ( )( )9 4 102
#6 Answer)
Y x x1 212 72 10
![Page 12: Product and Quotient Rule](https://reader035.vdocuments.us/reader035/viewer/2022070419/56815c3e550346895dca3bd7/html5/thumbnails/12.jpg)
• #7)
Y x x ( )( )3 6 94 3
#7 Answer)
Y x x1 6 3126 108
![Page 13: Product and Quotient Rule](https://reader035.vdocuments.us/reader035/viewer/2022070419/56815c3e550346895dca3bd7/html5/thumbnails/13.jpg)
• #8)
Y x x x ( )( )3 7 2 124 2
#8 Answer
Y x x x x1 4 3 230 144 42 168
![Page 14: Product and Quotient Rule](https://reader035.vdocuments.us/reader035/viewer/2022070419/56815c3e550346895dca3bd7/html5/thumbnails/14.jpg)
• #9)
#9 Answer
Y (x 3 7x 1)(5x 2)
Y1 20x 3 70x 6x 2 9
![Page 15: Product and Quotient Rule](https://reader035.vdocuments.us/reader035/viewer/2022070419/56815c3e550346895dca3bd7/html5/thumbnails/15.jpg)
• #10)
Y x 2(4 3x 3)
#10 Answer
Y1 15x 6
8x 3
![Page 16: Product and Quotient Rule](https://reader035.vdocuments.us/reader035/viewer/2022070419/56815c3e550346895dca3bd7/html5/thumbnails/16.jpg)
• #11)
Y x 3 ln x#11 Answer
Y1 x 2(1 3ln x)
![Page 17: Product and Quotient Rule](https://reader035.vdocuments.us/reader035/viewer/2022070419/56815c3e550346895dca3bd7/html5/thumbnails/17.jpg)
• #12)
#12 Answer
Y1 3x12 (2x sec2 x 3x tan x)
Y 6x32 tan x
![Page 18: Product and Quotient Rule](https://reader035.vdocuments.us/reader035/viewer/2022070419/56815c3e550346895dca3bd7/html5/thumbnails/18.jpg)
• #13)
#13 Answer
Y1 60x4 59 14(5x 2 2)2
Y 4x 3 7x5x 2 2
![Page 19: Product and Quotient Rule](https://reader035.vdocuments.us/reader035/viewer/2022070419/56815c3e550346895dca3bd7/html5/thumbnails/19.jpg)
• #14)
Y 7x 2
4ex x#14 Answer
Y1 7x(8ex 4xex x)(4ex x)2
![Page 20: Product and Quotient Rule](https://reader035.vdocuments.us/reader035/viewer/2022070419/56815c3e550346895dca3bd7/html5/thumbnails/20.jpg)
• #15)
Y 2x 1
#15 Answer
Y1 2(x 1)2
![Page 21: Product and Quotient Rule](https://reader035.vdocuments.us/reader035/viewer/2022070419/56815c3e550346895dca3bd7/html5/thumbnails/21.jpg)
• #16)
#16 Answer
Y1 x(3x 2)(3x 1)2
Y x 2
3x 1
![Page 22: Product and Quotient Rule](https://reader035.vdocuments.us/reader035/viewer/2022070419/56815c3e550346895dca3bd7/html5/thumbnails/22.jpg)
• #17)
Y 4sin x
2x cos x#17 Answer
Y1 8(x cos x sin x) 4(2x cos x)2
![Page 23: Product and Quotient Rule](https://reader035.vdocuments.us/reader035/viewer/2022070419/56815c3e550346895dca3bd7/html5/thumbnails/23.jpg)
• #18)
Y x 2 6x 39x 2 9x 4
#18 Answer
Y1 9x 3 53x 2 50x 3(9x 2 9x 4)2
![Page 24: Product and Quotient Rule](https://reader035.vdocuments.us/reader035/viewer/2022070419/56815c3e550346895dca3bd7/html5/thumbnails/24.jpg)
• #19)
Y 6x 2 2x 53x 2 3x 1
#19 Answer
Y1 12x2 18x 13
(3x 2 3x 1)2
![Page 25: Product and Quotient Rule](https://reader035.vdocuments.us/reader035/viewer/2022070419/56815c3e550346895dca3bd7/html5/thumbnails/25.jpg)
• #20
Y 7x 2 8x3x 2 6x
#20 Answer
Y1 150x 2
(3x 2 6x)2
![Page 26: Product and Quotient Rule](https://reader035.vdocuments.us/reader035/viewer/2022070419/56815c3e550346895dca3bd7/html5/thumbnails/26.jpg)
• #21)
Y 9x 3 4x5x 2 9x
#20 Answer
Y1 45x4 162x 3 20x 2
(5x 2 9x)2
![Page 27: Product and Quotient Rule](https://reader035.vdocuments.us/reader035/viewer/2022070419/56815c3e550346895dca3bd7/html5/thumbnails/27.jpg)
• #22)
Y 4x 2
12x 4#22 Answer
Y1 99x 5
12x 6
![Page 28: Product and Quotient Rule](https://reader035.vdocuments.us/reader035/viewer/2022070419/56815c3e550346895dca3bd7/html5/thumbnails/28.jpg)
• #23)
Y 7x 2 6x 43x 3 2x
#23 Answer
Y1 21x 4 36x 3 22x 2 8(3x 3 2x)2
![Page 29: Product and Quotient Rule](https://reader035.vdocuments.us/reader035/viewer/2022070419/56815c3e550346895dca3bd7/html5/thumbnails/29.jpg)
• #24)
Y 6x 3 5x 2
5x 4#24 Answer
Y1 30x 6 50x 5
5x 6
![Page 30: Product and Quotient Rule](https://reader035.vdocuments.us/reader035/viewer/2022070419/56815c3e550346895dca3bd7/html5/thumbnails/30.jpg)
• #25)
Y 5x 2 sin x cos x
#25 Answer
Y1 5x 2 cosx sin x 10x sin x cos x
![Page 31: Product and Quotient Rule](https://reader035.vdocuments.us/reader035/viewer/2022070419/56815c3e550346895dca3bd7/html5/thumbnails/31.jpg)
• #26)
Y x(3x 5)sin x
#26 Answer
Y1 3x 2 cos x 5x cos x 6x sin x 5sin x
![Page 32: Product and Quotient Rule](https://reader035.vdocuments.us/reader035/viewer/2022070419/56815c3e550346895dca3bd7/html5/thumbnails/32.jpg)
• #27)
Y x 4 sin x
#27 Answer
Y1 x 4 cos x 4x 3 sin x
![Page 33: Product and Quotient Rule](https://reader035.vdocuments.us/reader035/viewer/2022070419/56815c3e550346895dca3bd7/html5/thumbnails/33.jpg)
• #28)
4
2
124xxY
#28 Answer
6
51
1299xxY
![Page 34: Product and Quotient Rule](https://reader035.vdocuments.us/reader035/viewer/2022070419/56815c3e550346895dca3bd7/html5/thumbnails/34.jpg)
• #29)
23
2
7643xxxxY
#29 Answer
223
2341
)76(284818
xxxxxY
![Page 35: Product and Quotient Rule](https://reader035.vdocuments.us/reader035/viewer/2022070419/56815c3e550346895dca3bd7/html5/thumbnails/35.jpg)
• #30)
)310)(272( 523 xxxxY
#30 Answer
6632410010350100 2345671 xxxxxxY
)310)(272( 523 xxxxY
![Page 36: Product and Quotient Rule](https://reader035.vdocuments.us/reader035/viewer/2022070419/56815c3e550346895dca3bd7/html5/thumbnails/36.jpg)
• #31)
5104512 231 xxxY
)25)(13( 22 xxxY
#31 Answer
![Page 37: Product and Quotient Rule](https://reader035.vdocuments.us/reader035/viewer/2022070419/56815c3e550346895dca3bd7/html5/thumbnails/37.jpg)
• #32)
)4)(( 32 xxY#32 Answer
xxxY 83 341
![Page 38: Product and Quotient Rule](https://reader035.vdocuments.us/reader035/viewer/2022070419/56815c3e550346895dca3bd7/html5/thumbnails/38.jpg)
19104177224 231 xxxY
• #33)
)358)(237( 22 xxxxY
#33 Answer
![Page 39: Product and Quotient Rule](https://reader035.vdocuments.us/reader035/viewer/2022070419/56815c3e550346895dca3bd7/html5/thumbnails/39.jpg)
• #34)
789814740 231 xxxY)392)(825( 22 xxxxY
#34 Answer
789814740 231 xxxY
![Page 40: Product and Quotient Rule](https://reader035.vdocuments.us/reader035/viewer/2022070419/56815c3e550346895dca3bd7/html5/thumbnails/40.jpg)
• #35)
#35 Answer
49806324 231 xxxY
)833)(352( 22 xxxxY
![Page 41: Product and Quotient Rule](https://reader035.vdocuments.us/reader035/viewer/2022070419/56815c3e550346895dca3bd7/html5/thumbnails/41.jpg)
• #36)
4112812632 231 xxxY)582)(254( 22 xxxxY
#36 Answer
4112812632 231 xxxY
![Page 42: Product and Quotient Rule](https://reader035.vdocuments.us/reader035/viewer/2022070419/56815c3e550346895dca3bd7/html5/thumbnails/42.jpg)
• #37)
)553)(676( 22 xxxxY
#37 Answer
6516615372 231 xxxY
![Page 43: Product and Quotient Rule](https://reader035.vdocuments.us/reader035/viewer/2022070419/56815c3e550346895dca3bd7/html5/thumbnails/43.jpg)
• #38)
)82)(74( 22 xxxxY
#38 Answer
xxxY 11213832 231
![Page 44: Product and Quotient Rule](https://reader035.vdocuments.us/reader035/viewer/2022070419/56815c3e550346895dca3bd7/html5/thumbnails/44.jpg)
• #39)
)7)(6( 43 xxY )7)(6( 43 xxY #39 Answer
61 294xY
![Page 45: Product and Quotient Rule](https://reader035.vdocuments.us/reader035/viewer/2022070419/56815c3e550346895dca3bd7/html5/thumbnails/45.jpg)
• #40)
22
21
)54(2
xxxY
xxxxY5476
2
2
#40 Answer