1. Calculus Rules

2. Calculus Rules
d  u  vu   uv
 
3. Quotient Rule
dx  v  v2

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. 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. 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. 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. 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. 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. 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. 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. 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. 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. d  k   kv
4. Reciprocal Rule   2
dx  v  v

14. d  k   kv
4. Reciprocal Rule   2
dx  v  v
“MINUS the DERIVATIVE on the FUNCTION SQUARED”

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. 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. 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. 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. 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. 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. 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