11X1 T09 05 product rule (2010)
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Transcript of 11X1 T09 05 product rule (2010)
![Page 1: 11X1 T09 05 product rule (2010)](https://reader033.fdocuments.in/reader033/viewer/2022052910/559c266f1a28ab392c8b4645/html5/thumbnails/1.jpg)
Calculus Rules
![Page 2: 11X1 T09 05 product rule (2010)](https://reader033.fdocuments.in/reader033/viewer/2022052910/559c266f1a28ab392c8b4645/html5/thumbnails/2.jpg)
Calculus Rules2. Product Rule d uv uv vu
dx
![Page 3: 11X1 T09 05 product rule (2010)](https://reader033.fdocuments.in/reader033/viewer/2022052910/559c266f1a28ab392c8b4645/html5/thumbnails/3.jpg)
Calculus Rules2. Product Rule
“Write down the FIRST and DIFF the SECOND, PLUS write down the SECOND and DIFF the FIRST”
d uv uv vudx
![Page 4: 11X1 T09 05 product rule (2010)](https://reader033.fdocuments.in/reader033/viewer/2022052910/559c266f1a28ab392c8b4645/html5/thumbnails/4.jpg)
Calculus Rules2. Product Rule
“Write down the FIRST and DIFF the SECOND, PLUS write down the SECOND and DIFF the FIRST”
7 9e.g. 6i y x x
d uv uv vudx
![Page 5: 11X1 T09 05 product rule (2010)](https://reader033.fdocuments.in/reader033/viewer/2022052910/559c266f1a28ab392c8b4645/html5/thumbnails/5.jpg)
Calculus Rules2. Product Rule
“Write down the FIRST and DIFF the SECOND, PLUS write down the SECOND and DIFF the FIRST”
7 9e.g. 6i y x x
7 8 9 69 6 7dy x x x xdx
d uv uv vudx
![Page 6: 11X1 T09 05 product rule (2010)](https://reader033.fdocuments.in/reader033/viewer/2022052910/559c266f1a28ab392c8b4645/html5/thumbnails/6.jpg)
Calculus Rules2. Product Rule
“Write down the FIRST and DIFF the SECOND, PLUS write down the SECOND and DIFF the FIRST”
7 9e.g. 6i y x x
7 8 9 69 6 7dy x x x xdx
15 15 69 7 42x x x
d uv uv vudx
![Page 7: 11X1 T09 05 product rule (2010)](https://reader033.fdocuments.in/reader033/viewer/2022052910/559c266f1a28ab392c8b4645/html5/thumbnails/7.jpg)
Calculus Rules2. Product Rule
“Write down the FIRST and DIFF the SECOND, PLUS write down the SECOND and DIFF the FIRST”
7 9e.g. 6i y x x
7 8 9 69 6 7dy x x x xdx
15 15 69 7 42x x x
d uv uv vudx
15 616 42x x
![Page 8: 11X1 T09 05 product rule (2010)](https://reader033.fdocuments.in/reader033/viewer/2022052910/559c266f1a28ab392c8b4645/html5/thumbnails/8.jpg)
Calculus Rules2. Product Rule
“Write down the FIRST and DIFF the SECOND, PLUS write down the SECOND and DIFF the FIRST”
7 9e.g. 6i y x x
7 8 9 69 6 7dy x x x xdx
15 15 69 7 42x x x
2 2 3ii y x x
d uv uv vudx
15 616 42x x
![Page 9: 11X1 T09 05 product rule (2010)](https://reader033.fdocuments.in/reader033/viewer/2022052910/559c266f1a28ab392c8b4645/html5/thumbnails/9.jpg)
Calculus Rules2. Product Rule
“Write down the FIRST and DIFF the SECOND, PLUS write down the SECOND and DIFF the FIRST”
7 9e.g. 6i y x x
7 8 9 69 6 7dy x x x xdx
15 15 69 7 42x x x
2 2 3ii y x x
2 2 2 3 1dy x xdx
d uv uv vudx
15 616 42x x
![Page 10: 11X1 T09 05 product rule (2010)](https://reader033.fdocuments.in/reader033/viewer/2022052910/559c266f1a28ab392c8b4645/html5/thumbnails/10.jpg)
Calculus Rules2. Product Rule
“Write down the FIRST and DIFF the SECOND, PLUS write down the SECOND and DIFF the FIRST”
7 9e.g. 6i y x x
7 8 9 69 6 7dy x x x xdx
15 15 69 7 42x x x
2 2 3ii y x x
2 2 2 3 1dy x xdx
2 4 2 3x x
d uv uv vudx
15 616 42x x
![Page 11: 11X1 T09 05 product rule (2010)](https://reader033.fdocuments.in/reader033/viewer/2022052910/559c266f1a28ab392c8b4645/html5/thumbnails/11.jpg)
Calculus Rules2. Product Rule
“Write down the FIRST and DIFF the SECOND, PLUS write down the SECOND and DIFF the FIRST”
7 9e.g. 6i y x x
7 8 9 69 6 7dy x x x xdx
15 15 69 7 42x x x
2 2 3ii y x x
2 2 2 3 1dy x xdx
2 4 2 3x x
d uv uv vudx
15 616 42x x 4 7x
![Page 12: 11X1 T09 05 product rule (2010)](https://reader033.fdocuments.in/reader033/viewer/2022052910/559c266f1a28ab392c8b4645/html5/thumbnails/12.jpg)
Calculus Rules2. Product Rule
“Write down the FIRST and DIFF the SECOND, PLUS write down the SECOND and DIFF the FIRST”
7 9e.g. 6i y x x
7 8 9 69 6 7dy x x x xdx
15 15 69 7 42x x x
2 2 3ii y x x
2 2 2 3 1dy x xdx
2 4 2 3x x
7 3 2 3 7diii x x xdx
d uv uv vudx
15 616 42x x 4 7x
![Page 13: 11X1 T09 05 product rule (2010)](https://reader033.fdocuments.in/reader033/viewer/2022052910/559c266f1a28ab392c8b4645/html5/thumbnails/13.jpg)
Calculus Rules2. Product Rule
“Write down the FIRST and DIFF the SECOND, PLUS write down the SECOND and DIFF the FIRST”
7 9e.g. 6i y x x
7 8 9 69 6 7dy x x x xdx
15 15 69 7 42x x x
2 2 3ii y x x
2 2 2 3 1dy x xdx
2 4 2 3x x
7 3 2 3 7diii x x xdx
7 3 2 6 26 3 7 7 3x x x x x x
d uv uv vudx
15 616 42x x 4 7x
![Page 14: 11X1 T09 05 product rule (2010)](https://reader033.fdocuments.in/reader033/viewer/2022052910/559c266f1a28ab392c8b4645/html5/thumbnails/14.jpg)
Calculus Rules2. Product Rule
“Write down the FIRST and DIFF the SECOND, PLUS write down the SECOND and DIFF the FIRST”
7 9e.g. 6i y x x
7 8 9 69 6 7dy x x x xdx
15 15 69 7 42x x x
2 2 3ii y x x
2 2 2 3 1dy x xdx
2 4 2 3x x
7 3 2 3 7diii x x xdx
7 3 2 6 26 3 7 7 3x x x x x x 8 4 8 4 6 26 6 21 9 49 21x x x x x x
d uv uv vudx
15 616 42x x 4 7x
![Page 15: 11X1 T09 05 product rule (2010)](https://reader033.fdocuments.in/reader033/viewer/2022052910/559c266f1a28ab392c8b4645/html5/thumbnails/15.jpg)
Calculus Rules2. Product Rule
“Write down the FIRST and DIFF the SECOND, PLUS write down the SECOND and DIFF the FIRST”
7 9e.g. 6i y x x
7 8 9 69 6 7dy x x x xdx
15 15 69 7 42x x x
2 2 3ii y x x
2 2 2 3 1dy x xdx
2 4 2 3x x
7 3 2 3 7diii x x xdx
7 3 2 6 26 3 7 7 3x x x x x x 8 4 8 4 6 26 6 21 9 49 21x x x x x x
d uv uv vudx
15 616 42x x 4 7x
8 6 4 227 49 15 21x x x x
![Page 16: 11X1 T09 05 product rule (2010)](https://reader033.fdocuments.in/reader033/viewer/2022052910/559c266f1a28ab392c8b4645/html5/thumbnails/16.jpg)
52 3 4iv y x x
![Page 17: 11X1 T09 05 product rule (2010)](https://reader033.fdocuments.in/reader033/viewer/2022052910/559c266f1a28ab392c8b4645/html5/thumbnails/17.jpg)
4 52 23 5 4 2 4 3dy x x x xdx
52 3 4iv y x x
![Page 18: 11X1 T09 05 product rule (2010)](https://reader033.fdocuments.in/reader033/viewer/2022052910/559c266f1a28ab392c8b4645/html5/thumbnails/18.jpg)
4 52 23 5 4 2 4 3dy x x x xdx
52 3 4iv y x x
4 52 2 230 4 3 4x x x
![Page 19: 11X1 T09 05 product rule (2010)](https://reader033.fdocuments.in/reader033/viewer/2022052910/559c266f1a28ab392c8b4645/html5/thumbnails/19.jpg)
4 52 23 5 4 2 4 3dy x x x xdx
52 3 4iv y x x
4 52 2 230 4 3 4x x x
42 2 24 30 3 4x x x
![Page 20: 11X1 T09 05 product rule (2010)](https://reader033.fdocuments.in/reader033/viewer/2022052910/559c266f1a28ab392c8b4645/html5/thumbnails/20.jpg)
4 52 23 5 4 2 4 3dy x x x xdx
52 3 4iv y x x
4 52 2 230 4 3 4x x x
42 2 24 30 3 4x x x
42 24 33 12x x
![Page 21: 11X1 T09 05 product rule (2010)](https://reader033.fdocuments.in/reader033/viewer/2022052910/559c266f1a28ab392c8b4645/html5/thumbnails/21.jpg)
4 52 23 5 4 2 4 3dy x x x xdx
52 3 4iv y x x
4 52 2 230 4 3 4x x x
42 2 24 30 3 4x x x
42 24 33 12x x
42 23 4 11 4x x
![Page 22: 11X1 T09 05 product rule (2010)](https://reader033.fdocuments.in/reader033/viewer/2022052910/559c266f1a28ab392c8b4645/html5/thumbnails/22.jpg)
4 52 23 5 4 2 4 3dy x x x xdx
52 3 4iv y x x
2 2 1v y x x
4 52 2 230 4 3 4x x x
42 2 24 30 3 4x x x
42 24 33 12x x
42 23 4 11 4x x
![Page 23: 11X1 T09 05 product rule (2010)](https://reader033.fdocuments.in/reader033/viewer/2022052910/559c266f1a28ab392c8b4645/html5/thumbnails/23.jpg)
4 52 23 5 4 2 4 3dy x x x xdx
52 3 4iv y x x
2 2 1v y x x
4 52 2 230 4 3 4x x x
42 2 24 30 3 4x x x
42 24 33 12x x
42 23 4 11 4x x
122 2 1x x
![Page 24: 11X1 T09 05 product rule (2010)](https://reader033.fdocuments.in/reader033/viewer/2022052910/559c266f1a28ab392c8b4645/html5/thumbnails/24.jpg)
4 52 23 5 4 2 4 3dy x x x xdx
52 3 4iv y x x
2 2 1v y x x
1 12 2
12 2 1 2 2 1 22
dy x x xdx
4 52 2 230 4 3 4x x x
42 2 24 30 3 4x x x
42 24 33 12x x
42 23 4 11 4x x
122 2 1x x
![Page 25: 11X1 T09 05 product rule (2010)](https://reader033.fdocuments.in/reader033/viewer/2022052910/559c266f1a28ab392c8b4645/html5/thumbnails/25.jpg)
4 52 23 5 4 2 4 3dy x x x xdx
52 3 4iv y x x
2 2 1v y x x
1 12 2
12 2 1 2 2 1 22
dy x x xdx
4 52 2 230 4 3 4x x x
42 2 24 30 3 4x x x
42 24 33 12x x
42 23 4 11 4x x
122 2 1x x
1 12 22 2 1 2 2 1x x x
![Page 26: 11X1 T09 05 product rule (2010)](https://reader033.fdocuments.in/reader033/viewer/2022052910/559c266f1a28ab392c8b4645/html5/thumbnails/26.jpg)
4 52 23 5 4 2 4 3dy x x x xdx
52 3 4iv y x x
2 2 1v y x x
1 12 2
12 2 1 2 2 1 22
dy x x xdx
4 52 2 230 4 3 4x x x
42 2 24 30 3 4x x x
42 24 33 12x x
42 23 4 11 4x x
122 2 1x x
1 12 22 2 1 2 2 1x x x
122 2 1 2 1x x x
![Page 27: 11X1 T09 05 product rule (2010)](https://reader033.fdocuments.in/reader033/viewer/2022052910/559c266f1a28ab392c8b4645/html5/thumbnails/27.jpg)
4 52 23 5 4 2 4 3dy x x x xdx
52 3 4iv y x x
2 2 1v y x x
1 12 2
12 2 1 2 2 1 22
dy x x xdx
4 52 2 230 4 3 4x x x
42 2 24 30 3 4x x x
42 24 33 12x x
42 23 4 11 4x x
122 2 1x x
1 12 22 2 1 2 2 1x x x
122 2 1 2 1x x x
122 2 1 3 1x x
![Page 28: 11X1 T09 05 product rule (2010)](https://reader033.fdocuments.in/reader033/viewer/2022052910/559c266f1a28ab392c8b4645/html5/thumbnails/28.jpg)
4 52 23 5 4 2 4 3dy x x x xdx
52 3 4iv y x x
2 2 1v y x x
1 12 2
12 2 1 2 2 1 22
dy x x xdx
4 52 2 230 4 3 4x x x
42 2 24 30 3 4x x x
42 24 33 12x x
42 23 4 11 4x x
122 2 1x x
1 12 22 2 1 2 2 1x x x
122 2 1 2 1x x x
122 2 1 3 1x x
2 3 12 1xdy
dx x
![Page 29: 11X1 T09 05 product rule (2010)](https://reader033.fdocuments.in/reader033/viewer/2022052910/559c266f1a28ab392c8b4645/html5/thumbnails/29.jpg)
4 52 23 5 4 2 4 3dy x x x xdx
52 3 4iv y x x
2 2 1v y x x
1 12 2
12 2 1 2 2 1 22
dy x x xdx
Exercise 7F; 1ac, 2bdf,3a, 4ad, 5, 6ac,
7, 9, 13a*
4 52 2 230 4 3 4x x x
42 2 24 30 3 4x x x
42 24 33 12x x
42 23 4 11 4x x
122 2 1x x
1 12 22 2 1 2 2 1x x x
122 2 1 2 1x x x
122 2 1 3 1x x
2 3 12 1xdy
dx x