11X1 T09 06 quotient & reciprocal rules (2011)
-
Upload
nigel-simmons -
Category
Technology
-
view
540 -
download
0
Transcript of 11X1 T09 06 quotient & reciprocal rules (2011)
![Page 1: 11X1 T09 06 quotient & reciprocal rules (2011)](https://reader035.fdocuments.us/reader035/viewer/2022081603/559ebbe61a28ab832a8b46a0/html5/thumbnails/1.jpg)
Calculus Rules
![Page 2: 11X1 T09 06 quotient & reciprocal rules (2011)](https://reader035.fdocuments.us/reader035/viewer/2022081603/559ebbe61a28ab832a8b46a0/html5/thumbnails/2.jpg)
Calculus Rules3. Quotient Rule
2 d u vu uvdx v v
![Page 3: 11X1 T09 06 quotient & reciprocal rules (2011)](https://reader035.fdocuments.us/reader035/viewer/2022081603/559ebbe61a28ab832a8b46a0/html5/thumbnails/3.jpg)
Calculus Rules3. 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 uvdx v v
![Page 4: 11X1 T09 06 quotient & reciprocal rules (2011)](https://reader035.fdocuments.us/reader035/viewer/2022081603/559ebbe61a28ab832a8b46a0/html5/thumbnails/4.jpg)
Calculus Rules3. 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 2xi y
x
2 d u vu uvdx v v
![Page 5: 11X1 T09 06 quotient & reciprocal rules (2011)](https://reader035.fdocuments.us/reader035/viewer/2022081603/559ebbe61a28ab832a8b46a0/html5/thumbnails/5.jpg)
Calculus Rules3. 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 2xi y
x
2
1 2 1 21 2x xdy
dx x
2 d u vu uvdx v v
![Page 6: 11X1 T09 06 quotient & reciprocal rules (2011)](https://reader035.fdocuments.us/reader035/viewer/2022081603/559ebbe61a28ab832a8b46a0/html5/thumbnails/6.jpg)
Calculus Rules3. 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 2xi y
x
2
1 2 1 21 2x xdy
dx x
21 2 2
1 2x x
x
2 d u vu uvdx v v
![Page 7: 11X1 T09 06 quotient & reciprocal rules (2011)](https://reader035.fdocuments.us/reader035/viewer/2022081603/559ebbe61a28ab832a8b46a0/html5/thumbnails/7.jpg)
Calculus Rules3. 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 2xi y
x
2
1 2 1 21 2x xdy
dx x
21 2 2
1 2x x
x
2 d u vu uvdx v v
21
1 2x
![Page 8: 11X1 T09 06 quotient & reciprocal rules (2011)](https://reader035.fdocuments.us/reader035/viewer/2022081603/559ebbe61a28ab832a8b46a0/html5/thumbnails/8.jpg)
Calculus Rules3. 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 2xi y
x
2
1 2 1 21 2x xdy
dx x
21 2 2
1 2x x
x
2
2 4
xii yx
2 d u vu uvdx v v
21
1 2x
![Page 9: 11X1 T09 06 quotient & reciprocal rules (2011)](https://reader035.fdocuments.us/reader035/viewer/2022081603/559ebbe61a28ab832a8b46a0/html5/thumbnails/9.jpg)
Calculus Rules3. 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 2xi y
x
2
1 2 1 21 2x xdy
dx x
21 2 2
1 2x x
x
2
2 4
xii yx
1 12 22 2
2
14 2 2 4 224
x x x xdydx x
2 d u vu uvdx v v
21
1 2x
![Page 10: 11X1 T09 06 quotient & reciprocal rules (2011)](https://reader035.fdocuments.us/reader035/viewer/2022081603/559ebbe61a28ab832a8b46a0/html5/thumbnails/10.jpg)
Calculus Rules3. 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 2xi y
x
2
1 2 1 21 2x xdy
dx x
21 2 2
1 2x x
x
2
2 4
xii yx
1 12 22 2
2
14 2 2 4 224
x x x xdydx x
2 d u vu uvdx v v
21
1 2x
1 12 2 22 2
2
2 4 2 44
x x xx
![Page 11: 11X1 T09 06 quotient & reciprocal rules (2011)](https://reader035.fdocuments.us/reader035/viewer/2022081603/559ebbe61a28ab832a8b46a0/html5/thumbnails/11.jpg)
Calculus Rules3. 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 2xi y
x
2
1 2 1 21 2x xdy
dx x
21 2 2
1 2x x
x
2
2 4
xii yx
1 12 22 2
2
14 2 2 4 224
x x x xdydx x
2 d u vu uvdx v v
21
1 2x
1 12 2 22 2
2
2 4 2 44
x x xx
12 2 22
2
2 4 44
x x xx
![Page 12: 11X1 T09 06 quotient & reciprocal rules (2011)](https://reader035.fdocuments.us/reader035/viewer/2022081603/559ebbe61a28ab832a8b46a0/html5/thumbnails/12.jpg)
Calculus Rules3. 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 2xi y
x
2
1 2 1 21 2x xdy
dx x
21 2 2
1 2x x
x
2
2 4
xii yx
1 12 22 2
2
14 2 2 4 224
x x x xdydx x
2 d u vu uvdx v v
21
1 2x
1 12 2 22 2
2
2 4 2 44
x x xx
12 2 22
2
2 4 44
x x xx
2 2
84 4x x
![Page 13: 11X1 T09 06 quotient & reciprocal rules (2011)](https://reader035.fdocuments.us/reader035/viewer/2022081603/559ebbe61a28ab832a8b46a0/html5/thumbnails/13.jpg)
4. Reciprocal Rule 2 d k kvdx v v
![Page 14: 11X1 T09 06 quotient & reciprocal rules (2011)](https://reader035.fdocuments.us/reader035/viewer/2022081603/559ebbe61a28ab832a8b46a0/html5/thumbnails/14.jpg)
4. Reciprocal Rule 2 d k kvdx v v
“MINUS the DERIVATIVE on the FUNCTION SQUARED”
![Page 15: 11X1 T09 06 quotient & reciprocal rules (2011)](https://reader035.fdocuments.us/reader035/viewer/2022081603/559ebbe61a28ab832a8b46a0/html5/thumbnails/15.jpg)
4. Reciprocal Rule 2 d k kvdx v v
“MINUS the DERIVATIVE on the FUNCTION SQUARED”
21e.g. i yx
![Page 16: 11X1 T09 06 quotient & reciprocal rules (2011)](https://reader035.fdocuments.us/reader035/viewer/2022081603/559ebbe61a28ab832a8b46a0/html5/thumbnails/16.jpg)
4. Reciprocal Rule 2 d k kvdx v v
“MINUS the DERIVATIVE on the FUNCTION SQUARED”
21e.g. i yx
42dy x
dx x
![Page 17: 11X1 T09 06 quotient & reciprocal rules (2011)](https://reader035.fdocuments.us/reader035/viewer/2022081603/559ebbe61a28ab832a8b46a0/html5/thumbnails/17.jpg)
4. Reciprocal Rule 2 d k kvdx v v
“MINUS the DERIVATIVE on the FUNCTION SQUARED”
21e.g. i yx
42dy x
dx x
32
x
![Page 18: 11X1 T09 06 quotient & reciprocal rules (2011)](https://reader035.fdocuments.us/reader035/viewer/2022081603/559ebbe61a28ab832a8b46a0/html5/thumbnails/18.jpg)
4. Reciprocal Rule 2 d k kvdx v v
“MINUS the DERIVATIVE on the FUNCTION SQUARED”
21e.g. i yx
42dy x
dx x
32
x
26
4 3ii y
x
![Page 19: 11X1 T09 06 quotient & reciprocal rules (2011)](https://reader035.fdocuments.us/reader035/viewer/2022081603/559ebbe61a28ab832a8b46a0/html5/thumbnails/19.jpg)
4. Reciprocal Rule 2 d k kvdx v v
“MINUS the DERIVATIVE on the FUNCTION SQUARED”
21e.g. i yx
42dy x
dx x
32
x
26
4 3ii y
x
22
6 8
4 3
xdydx x
![Page 20: 11X1 T09 06 quotient & reciprocal rules (2011)](https://reader035.fdocuments.us/reader035/viewer/2022081603/559ebbe61a28ab832a8b46a0/html5/thumbnails/20.jpg)
4. Reciprocal Rule 2 d k kvdx v v
“MINUS the DERIVATIVE on the FUNCTION SQUARED”
21e.g. i yx
42dy x
dx x
32
x
26
4 3ii y
x
22
6 8
4 3
xdydx x
22
484 3
xx
![Page 21: 11X1 T09 06 quotient & reciprocal rules (2011)](https://reader035.fdocuments.us/reader035/viewer/2022081603/559ebbe61a28ab832a8b46a0/html5/thumbnails/21.jpg)
4. Reciprocal Rule 2 d k kvdx v v
“MINUS the DERIVATIVE on the FUNCTION SQUARED”
21e.g. i yx
42dy x
dx x
32
x
26
4 3ii y
x
22
6 8
4 3
xdydx x
22
484 3
xx
Exercise 7G; 1aceg, 2, 4a, 6a, 8a