3. Calculus Rules
3. Quotient Rule
“SQUARE the BOTTOM, write down the BOTTOM and DIFF the
TOP, MINUS write down the TOP and DIFF the BOTTOM”
2
d u vu uv
dx v v
4. Calculus Rules
3. Quotient Rule
“SQUARE the BOTTOM, write down the BOTTOM and DIFF the
TOP, MINUS write down the TOP and DIFF the BOTTOM”
e.g.
1 2
x
i y
x
2
d u vu uv
dx v v
5. Calculus Rules
3. Quotient Rule
“SQUARE the BOTTOM, write down the BOTTOM and DIFF the
TOP, MINUS write down the TOP and DIFF the BOTTOM”
e.g.
1 2
x
i y
x
2
1 2 1 2
1 2
x xdy
dx x
2
d u vu uv
dx v v
6. Calculus Rules
3. Quotient Rule
“SQUARE the BOTTOM, write down the BOTTOM and DIFF the
TOP, MINUS write down the TOP and DIFF the BOTTOM”
e.g.
1 2
x
i y
x
2
1 2 1 2
1 2
x xdy
dx x
2
1 2 2
1 2
x x
x
2
d u vu uv
dx v v
7. Calculus Rules
3. Quotient Rule
“SQUARE the BOTTOM, write down the BOTTOM and DIFF the
TOP, MINUS write down the TOP and DIFF the BOTTOM”
e.g.
1 2
x
i y
x
2
1 2 1 2
1 2
x xdy
dx x
2
1 2 2
1 2
x x
x
2
d u vu uv
dx v v
2
1
1 2x
8. Calculus Rules
3. Quotient Rule
“SQUARE the BOTTOM, write down the BOTTOM and DIFF the
TOP, MINUS write down the TOP and DIFF the BOTTOM”
e.g.
1 2
x
i y
x
2
1 2 1 2
1 2
x xdy
dx x
2
1 2 2
1 2
x x
x
2
2
4
x
ii y
x
2
d u vu uv
dx v v
2
1
1 2x
9. Calculus Rules
3. Quotient Rule
“SQUARE the BOTTOM, write down the BOTTOM and DIFF the
TOP, MINUS write down the TOP and DIFF the BOTTOM”
e.g.
1 2
x
i y
x
2
1 2 1 2
1 2
x xdy
dx x
2
1 2 2
1 2
x x
x
2
2
4
x
ii y
x
1 1
2 22 2
2
1
4 2 2 4 2
2
4
x x x x
dy
dx x
2
d u vu uv
dx v v
2
1
1 2x
10. Calculus Rules
3. Quotient Rule
“SQUARE the BOTTOM, write down the BOTTOM and DIFF the
TOP, MINUS write down the TOP and DIFF the BOTTOM”
e.g.
1 2
x
i y
x
2
1 2 1 2
1 2
x xdy
dx x
2
1 2 2
1 2
x x
x
2
2
4
x
ii y
x
1 1
2 22 2
2
1
4 2 2 4 2
2
4
x x x x
dy
dx x
2
d u vu uv
dx v v
2
1
1 2x
1 1
2 2 22 2
2
2 4 2 4
4
x x x
x
11. Calculus Rules
3. Quotient Rule
“SQUARE the BOTTOM, write down the BOTTOM and DIFF the
TOP, MINUS write down the TOP and DIFF the BOTTOM”
e.g.
1 2
x
i y
x
2
1 2 1 2
1 2
x xdy
dx x
2
1 2 2
1 2
x x
x
2
2
4
x
ii y
x
1 1
2 22 2
2
1
4 2 2 4 2
2
4
x x x x
dy
dx x
2
d u vu uv
dx v v
2
1
1 2x
1 1
2 2 22 2
2
2 4 2 4
4
x x x
x
1
2 2 22
2
2 4 4
4
x x x
x
12. Calculus Rules
3. Quotient Rule
“SQUARE the BOTTOM, write down the BOTTOM and DIFF the
TOP, MINUS write down the TOP and DIFF the BOTTOM”
e.g.
1 2
x
i y
x
2
1 2 1 2
1 2
x xdy
dx x
2
1 2 2
1 2
x x
x
2
2
4
x
ii y
x
1 1
2 22 2
2
1
4 2 2 4 2
2
4
x x x x
dy
dx x
2
d u vu uv
dx v v
2
1
1 2x
1 1
2 2 22 2
2
2 4 2 4
4
x x x
x
1
2 2 22
2
2 4 4
4
x x x
x
2 2
8
4 4x x
14. 4. Reciprocal Rule 2
d k kv
dx v v
“MINUS the DERIVATIVE on the FUNCTION SQUARED”
15. 4. Reciprocal Rule 2
d k kv
dx v v
“MINUS the DERIVATIVE on the FUNCTION SQUARED”
2
1
e.g. i y
x
16. 4. Reciprocal Rule 2
d k kv
dx v v
“MINUS the DERIVATIVE on the FUNCTION SQUARED”
2
1
e.g. i y
x
4
2dy x
dx x
17. 4. Reciprocal Rule 2
d k kv
dx v v
“MINUS the DERIVATIVE on the FUNCTION SQUARED”
2
1
e.g. i y
x
4
2dy x
dx x
3
2
x
18. 4. Reciprocal Rule 2
d k kv
dx v v
“MINUS the DERIVATIVE on the FUNCTION SQUARED”
2
1
e.g. i y
x
4
2dy x
dx x
3
2
x
2
6
4 3
ii y
x
19. 4. Reciprocal Rule 2
d k kv
dx v v
“MINUS the DERIVATIVE on the FUNCTION SQUARED”
2
1
e.g. i y
x
4
2dy x
dx x
3
2
x
2
6
4 3
ii y
x
22
6 8
4 3
xdy
dx x
20. 4. Reciprocal Rule 2
d k kv
dx v v
“MINUS the DERIVATIVE on the FUNCTION SQUARED”
2
1
e.g. i y
x
4
2dy x
dx x
3
2
x
2
6
4 3
ii y
x
22
6 8
4 3
xdy
dx x
22
48
4 3
x
x
21. 4. Reciprocal Rule 2
d k kv
dx v v
“MINUS the DERIVATIVE on the FUNCTION SQUARED”
2
1
e.g. i y
x
4
2dy x
dx x
3
2
x
2
6
4 3
ii y
x
22
6 8
4 3
xdy
dx x
22
48
4 3
x
x
Exercise 7G; 1aceg, 2, 4a, 6a, 8a