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# 11X1 T09 05 product rule (2010)

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### 11X1 T09 05 product rule (2010)

1. 1. Calculus Rules
2. 2. Calculus Rules d 2. Product Rule  uv   uv  vu dx
3. 3. Calculus Rules d 2. Product Rule  uv   uv  vu dx “Write down the FIRST and DIFF the SECOND, PLUS write down the SECOND and DIFF the FIRST”
4. 4. Calculus Rulesd 2. Product Rule  uv   uv  vu dx “Write down the FIRST and DIFF the SECOND, PLUS write down the SECOND and DIFF the FIRST” e.g.  i  y  x 7  x 9  6 
5. 5. Calculus Rules d 2. Product Rule  uv   uv  vu dx “Write down the FIRST and DIFF the SECOND, PLUS write down the SECOND and DIFF the FIRST” e.g.  i  y  x 7  x 9  6    x 7  9 x8    x 9  6  7 x 6  dy dx
6. 6. Calculus Rules d 2. Product Rule  uv   uv  vu dx “Write down the FIRST and DIFF the SECOND, PLUS write down the SECOND and DIFF the FIRST” e.g.  i  y  x 7  x 9  6    x 7  9 x8    x 9  6  7 x 6  dy dx  9 x15  7 x15  42 x 6
7. 7. Calculus Rules d 2. Product Rule  uv   uv  vu dx “Write down the FIRST and DIFF the SECOND, PLUS write down the SECOND and DIFF the FIRST” e.g.  i  y  x 7  x 9  6    x 7  9 x8    x 9  6  7 x 6  dy dx  9 x15  7 x15  42 x 6  16 x15  42 x 6
8. 8. Calculus Rules d 2. Product Rule  uv   uv  vu dx “Write down the FIRST and DIFF the SECOND, PLUS write down the SECOND and DIFF the FIRST” e.g.  i  y  x 7  x 9  6   ii  y   x  2  2 x  3   x 7  9 x8    x 9  6  7 x 6  dy dx  9 x15  7 x15  42 x 6  16 x15  42 x 6
9. 9. Calculus Rules d 2. Product Rule  uv   uv  vu dx “Write down the FIRST and DIFF the SECOND, PLUS write down the SECOND and DIFF the FIRST” e.g.  i  y  x 7  x 9  6   ii  y   x  2  2 x  3 dy   x  9 x    x  6  7 x    x  2  2    2 x  31 dy 7 8 9 6 dx dx  9 x15  7 x15  42 x 6  16 x15  42 x 6
10. 10. Calculus Rules d 2. Product Rule  uv   uv  vu dx “Write down the FIRST and DIFF the SECOND, PLUS write down the SECOND and DIFF the FIRST” e.g.  i  y  x 7  x 9  6   ii  y   x  2  2 x  3 dy   x  9 x    x  6  7 x    x  2  2    2 x  31 dy 7 8 9 6 dx dx  9 x15  7 x15  42 x 6  2x  4  2x  3  16 x15  42 x 6
11. 11. Calculus Rules d 2. Product Rule  uv   uv  vu dx “Write down the FIRST and DIFF the SECOND, PLUS write down the SECOND and DIFF the FIRST” e.g.  i  y  x 7  x 9  6   ii  y   x  2  2 x  3 dy   x  9 x    x  6  7 x    x  2  2    2 x  31 dy 7 8 9 6 dx dx  9 x15  7 x15  42 x 6  2x  4  2x  3  16 x15  42 x 6  4x  7
12. 12. Calculus Rules d 2. Product Rule  uv   uv  vu dx “Write down the FIRST and DIFF the SECOND, PLUS write down the SECOND and DIFF the FIRST” e.g.  i  y  x 7  x 9  6   ii  y   x  2  2 x  3 dy   x  9 x    x  6  7 x    x  2  2    2 x  31 dy 7 8 9 6 dx dx  9 x15  7 x15  42 x 6  2x  4  2x  3  16 x15  42 x 6  4x  7  iii  d dx  x 7  x 3  3 x 2  7 
13. 13. Calculus Rules d 2. Product Rule  uv   uv  vu dx “Write down the FIRST and DIFF the SECOND, PLUS write down the SECOND and DIFF the FIRST” e.g.  i  y  x 7  x 9  6   ii  y   x  2  2 x  3 dy   x  9 x    x  6  7 x    x  2  2    2 x  31 dy 7 8 9 6 dx dx  9 x15  7 x15  42 x 6  2x  4  2x  3  16 x15  42 x 6  4x  7  iii  d dx  x 7  x 3  3 x 2  7    x 7  x 3   6 x    3 x 2  7  7 x 6  3 x 2 
14. 14. Calculus Rules d 2. Product Rule  uv   uv  vu dx “Write down the FIRST and DIFF the SECOND, PLUS write down the SECOND and DIFF the FIRST” e.g.  i  y  x 7  x 9  6   ii  y   x  2  2 x  3 dy   x  9 x    x  6  7 x    x  2  2    2 x  31 dy 7 8 9 6 dx dx  9 x15  7 x15  42 x 6  2x  4  2x  3  16 x15  42 x 6  4x  7  iii  d dx  x 7  x 3  3 x 2  7    x 7  x 3   6 x    3 x 2  7  7 x 6  3 x 2   6 x8  6 x 4  21x8  9 x 4  49 x 6  21x 2
15. 15. Calculus Rules d 2. Product Rule  uv   uv  vu dx “Write down the FIRST and DIFF the SECOND, PLUS write down the SECOND and DIFF the FIRST” e.g.  i  y  x 7  x 9  6   ii  y   x  2  2 x  3 dy   x  9 x    x  6  7 x    x  2  2    2 x  31 dy 7 8 9 6 dx dx  9 x15  7 x15  42 x 6  2x  4  2x  3  16 x15  42 x 6  4x  7  iii  d dx  x 7  x 3  3 x 2  7    x 7  x 3   6 x    3 x 2  7  7 x 6  3 x 2   6 x8  6 x 4  21x8  9 x 4  49 x 6  21x 2  27 x8  49 x 6  15 x 4  21x 2
16. 16.  iv  y  3x  x  4  2 5
17. 17.  iv  y  3x  x  4  2 5 dy dx  2 4    3 x  5  x  4   2 x    x  4   3 2 5
18. 18.  iv  y  3x  x  4  2 5 dy dx  2 4    3 x  5  x  4   2 x    x  4   3 2 5  30 x  x  4   3  x  4  2 2 4 2 5
19. 19.  iv  y  3x  x  4  2 5 dy dx  2 4    3 x  5  x  4   2 x    x  4   3 2 5  30 x  x  4   3  x  4  2 2 4 2 5   x  4  30 x 2  3  x 2  4  2 4
20. 20.  iv  y  3x  x  4  2 5 dy dx  2 4    3 x  5  x  4   2 x    x  4   3 2 5  30 x  x  4   3  x  4  2 2 4 2 5   x  4  30 x 2  3  x 2  4  2 4   x  4   33 x 2  12  2 4
21. 21.  iv  y  3x  x  4  2 5 dy dx  2 4    3 x  5  x  4   2 x    x  4   3 2 5  30 x  x  4   3  x  4  2 2 4 2 5   x  4  30 x 2  3  x 2  4  2 4   x  4   33 x 2  12  2 4  3  x  4  11x 2  4  2 4
22. 22.  iv  y  3x  x  4  2 5 dy dx  2 4    3 x  5  x  4   2 x    x  4   3 2 5  30 x  x  4   3  x  4  2 2 4 2 5   x  4  30 x 2  3  x 2  4  2 4   x  4   33 x 2  12  2 4  3  x  4  11x 2  4  2 4 v y  2x 2x 1
23. 23.  iv  y  3x  x  4  2 5 dy dx  2 4    3 x  5  x  4   2 x    x  4   3 2 5  30 x  x  4   3  x  4  2 2 4 2 5   x  4  30 x 2  3  x 2  4  2 4   x  4   33 x 2  12  2 4  3  x  4  11x 2  4  2 4 v y  2x 2x 1 1  2 x  2 x  1 2
24. 24.  iv  y  3x  x  4  2 5 dy dx  2 4    3 x  5  x  4   2 x    x  4   3 2 5  30 x  x  4   3  x  4  2 2 4 2 5   x  4  30 x 2  3  x 2  4  2 4   x  4   33 x 2  12  2 4  3  x  4  11x 2  4  2 4 v y  2x 2x 1 1  2 x  2 x  1 2 dy dx 1  1  1   2 x   2 x  1 2  2    2 x  1 2  2  2 
25. 25.  iv  y  3x  x  4  2 5 dy dx  2 4    3 x  5  x  4   2 x    x  4   3 2 5  30 x  x  4   3  x  4  2 2 4 2 5   x  4  30 x 2  3  x 2  4  2 4   x  4   33 x 2  12  2 4  3  x  4  11x 2  4  2 4 v y  2x 2x 1 1  2 x  2 x  1 2 dy dx 1  1  1   2 x   2 x  1 2  2    2 x  1 2  2  2  1 1   2 x  2 x  1 2  2  2 x  1 2 
26. 26.  iv  y  3x  x  4  2 5 dy dx  2 4 2 5    3 x  5  x  4   2 x    x  4   3  30 x  x  4   3  x  4  2 2 4 2 5   x  4  30 x 2  3  x 2  4  2 4   x  4   33 x 2  12  2 4  3  x  4  11x 2  4  2 4 v y  2x 2x 1 1  2 x  2 x  1 2 dy dx 1  1  1   2 x   2 x  1 2  2    2 x  1 2  2  2  1 1   2 x  2 x  1 2  2  2 x  1 2  1  2  2 x  1  2  x   2 x  1
27. 27.  iv  y  3x  x  4  2 5 dy dx  2 4 2 5    3 x  5  x  4   2 x    x  4   3  30 x  x  4   3  x  4  2 2 4 2 5   x  4  30 x 2  3  x 2  4  2 4   x  4   33 x 2  12  2 4  3  x  4  11x 2  4  2 4 v y  2x 2x 1 1  2 x  2 x  1 2 dy dx 1  1 1    2 x   2 x  1 2  2    2 x  1 2  2  2  1 1   2 x  2 x  1 2  2  2 x  1 2  1  2  2 x  1  2  x   2 x  1 1  2  2 x  1  3x  1  2
28. 28.  iv  y  3x  x  4  2 5 dy dx  2 4 2 5    3 x  5  x  4   2 x    x  4   3  30 x  x  4   3  x  4  2 2 4 2 5   x  4  30 x 2  3  x 2  4  2 4   x  4   33 x 2  12  2 4  3  x  4  11x 2  4  2 4 v y  2x 2x 1 1  2 x  2 x  1 2 dy dx 1  1 1    2 x   2 x  1 2  2    2 x  1 2  2  2  1 1   2 x  2 x  1 2  2  2 x  1 2  dy 2  3 x  1 1   2  2 x  1  2  x   2 x  1 dx 2x 1 1  2  2 x  1  3x  1  2
29. 29.  iv  y  3x  x  4  2 5 dy dx  2 4 2 5    3 x  5  x  4   2 x    x  4   3  30 x  x  4   3  x  4  2 2 4 2 5   x  4  30 x 2  3  x 2  4  2 4 Exercise 7F; 1ac, 2bdf,   x  4   33 x  12  2 4 2 3a, 4ad, 5, 6ac,  3  x  4  11x 2  4  4 2 7, 9, 13a* v y  2x 2x 1 1  2 x  2 x  1 2 dy dx 1  1 1    2 x   2 x  1 2  2    2 x  1 2  2  2  1 1   2 x  2 x  1 2  2  2 x  1 2  dy 2  3 x  1 1   2  2 x  1  2  x   2 x  1 dx 2x 1 1  2  2 x  1  3x  1  2