11X1 T09 06 quotient and reciprocal rules (2010)

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11X1 T09 06 quotient and reciprocal rules (2010)

  1. 1. Calculus Rules
  2. 2. Calculus Rules d  u  vu   uv   3. Quotient Rule dx  v  v2
  3. 3. Calculus Rules d  u  vu   uv   3. Quotient Rule dx  v  v2 “SQUARE the BOTTOM, write down the BOTTOM and DIFF the TOP, MINUS write down the TOP and DIFF the BOTTOM”
  4. 4. Calculus Rules d  u  vu   uv   3. Quotient Rule dx  v  v2 “SQUARE the BOTTOM, write down the BOTTOM and DIFF the TOP, MINUS write down the TOP and DIFF the BOTTOM” x e.g.  i  y  1 2x
  5. 5. Calculus Rules d  u  vu   uv   3. Quotient Rule dx  v  v2 “SQUARE the BOTTOM, write down the BOTTOM and DIFF the TOP, MINUS write down the TOP and DIFF the BOTTOM” x e.g.  i  y  1 2x dy 1  2 x 1   x  2   1  2 x  2 dx
  6. 6. Calculus Rules d  u  vu   uv   3. Quotient Rule dx  v  v2 “SQUARE the BOTTOM, write down the BOTTOM and DIFF the TOP, MINUS write down the TOP and DIFF the BOTTOM” x e.g.  i  y  1 2x dy 1  2 x 1   x  2   1  2 x  2 dx 1 2x  2x  1 2x 2
  7. 7. Calculus Rulesd  u  vu   uv   3. Quotient Rule dx  v  v2 “SQUARE the BOTTOM, write down the BOTTOM and DIFF the TOP, MINUS write down the TOP and DIFF the BOTTOM” x e.g.  i  y  1 2x dy 1  2 x 1   x  2   1  2 x  2 dx 1 2x  2x  1 2x 2 1  1  2x  2
  8. 8. Calculus Rulesd  u  vu   uv   3. Quotient Rule dx  v  v2 “SQUARE the BOTTOM, write down the BOTTOM and DIFF the TOP, MINUS write down the TOP and DIFF the BOTTOM” x 2x e.g.  i  y   ii  y  2 1 2x x 4 dy 1  2 x 1   x  2   1  2 x  2 dx 1 2x  2x  1 2x 2 1  1  2x  2
  9. 9. Calculus Rulesd  u  vu   uv   3. Quotient Rule dx  v  v2 “SQUARE the BOTTOM, write down the BOTTOM and DIFF the TOP, MINUS write down the TOP and DIFF the BOTTOM” x 2x e.g.  i  y   ii  y  2 1 2x x 4 dy 1  2 x 1   x  2  1 2  1 1  x  4      2  x  4     2 2  2x  2 2 2x 1  2 x    2 dx dy  1 2x  2x dx  x2  4  1 2x 2 1  1  2x  2
  10. 10. Calculus Rules d  u  vu   uv   3. Quotient Rule dx  v  v2 “SQUARE the BOTTOM, write down the BOTTOM and DIFF the TOP, MINUS write down the TOP and DIFF the BOTTOM” x 2x e.g.  i  y   ii  y  2 1 2x x 4 dy 1  2 x 1   x  2  1 2  1 1  x  4      2  x  4     2 2  2x  2 2 2x 1  2 x    2 dx dy  1 2x  2x dx  x 2  4  1  1 1  2 x  2 2  x  42  2 x2  x2  4 2 2   1  x2  4 1  2x  2
  11. 11. Calculus Rules d  u  vu   uv   3. Quotient Rule dx  v  v2 “SQUARE the BOTTOM, write down the BOTTOM and DIFF the TOP, MINUS write down the TOP and DIFF the BOTTOM” x 2x e.g.  i  y   ii  y  2 1 2x x 4 dy 1  2 x 1   x  2  1 2  1 1  x  4      2  x  4     2 2  2x  2 2 2x 1  2 x    2 dx dy  1 2x  2x dx  x 2  4  1  1 1  2 x  2 2  x  42  2 x2  x2  4 2 2   1  x2  4 1  2x  2 2  x 2  4  2  x 2  4   x 2  1    x2  4
  12. 12. Calculus Rules d  u  vu   uv   3. Quotient Rule dx  v  v2 “SQUARE the BOTTOM, write down the BOTTOM and DIFF the TOP, MINUS write down the TOP and DIFF the BOTTOM” x 2x e.g.  i  y   ii  y  2 1 2x x 4 dy 1  2 x 1   x  2  1 2  1 1  x  4      2  x  4     2 2  2x  2 2 2x 1  2 x    2 dx dy  1 2x  2x dx  x 2  4  1  1 1  2 x  2 2  x  42  2 x2  x2  4 2 2   1  x2  4 1  2x  2 2  x 2  4  2  x 2  4   x 2  1   8  x2  4   x2  4 x2  4
  13. 13. d  k   kv 4. Reciprocal Rule   2 dx  v  v
  14. 14. d  k   kv 4. Reciprocal Rule   2 dx  v  v “MINUS the DERIVATIVE on the FUNCTION SQUARED”
  15. 15. d  k   kv 4. Reciprocal Rule   2 dx  v  v “MINUS the DERIVATIVE on the FUNCTION SQUARED” 1 e.g.  i  y  x2
  16. 16. d  k   kv 4. Reciprocal Rule   2 dx  v  v “MINUS the DERIVATIVE on the FUNCTION SQUARED” 1 e.g.  i  y  x2 dy 2 x  4 dx x
  17. 17. d  k   kv 4. Reciprocal Rule   2 dx  v  v “MINUS the DERIVATIVE on the FUNCTION SQUARED” 1 e.g.  i  y  x2 dy 2 x  4 dx x 2  3 x
  18. 18. d  k   kv 4. Reciprocal Rule   2 dx  v  v “MINUS the DERIVATIVE on the FUNCTION SQUARED” 1 6 e.g.  i  y   ii  y  x2 4 x2  3 dy 2 x  4 dx x 2  3 x
  19. 19. d  k   kv 4. Reciprocal Rule   2 dx  v  v “MINUS the DERIVATIVE on the FUNCTION SQUARED” 1 6 e.g.  i  y   ii  y  x2 4 x2  3 dy 2 x dy 6  8 x   4  dx x dx  4 x 2  32 2  3 x
  20. 20. d  k   kv 4. Reciprocal Rule   2 dx  v  v “MINUS the DERIVATIVE on the FUNCTION SQUARED” 1 6 e.g.  i  y   ii  y  x2 4 x2  3 dy 2 x dy 6  8 x   4  dx x dx  4 x 2  32 2 48 x  3   4 x  3 2 x 2
  21. 21. d  k   kv 4. Reciprocal Rule   2 dx  v  v “MINUS the DERIVATIVE on the FUNCTION SQUARED” 1 6 e.g.  i  y   ii  y  x2 4 x2  3 dy 2 x dy 6  8 x   4  dx x dx  4 x 2  32 2 48 x  3   4 x  3 2 x 2 Exercise 7G; 1aceg, 2, 4a, 6a, 8a

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