11x1 t08 06 quotient & reciprocal rules
TRANSCRIPT
![Page 1: 11X1 T08 06 quotient & reciprocal rules](https://reader033.vdocuments.us/reader033/viewer/2022060117/55852446d8b42aa86c8b5026/html5/thumbnails/1.jpg)
Calculus Rules
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Calculus Rules3. Quotient Rule
2 d u vu uvdx v v
![Page 3: 11X1 T08 06 quotient & reciprocal rules](https://reader033.vdocuments.us/reader033/viewer/2022060117/55852446d8b42aa86c8b5026/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 T08 06 quotient & reciprocal rules](https://reader033.vdocuments.us/reader033/viewer/2022060117/55852446d8b42aa86c8b5026/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 2x
i yx
2 d u vu uvdx v v
![Page 5: 11X1 T08 06 quotient & reciprocal rules](https://reader033.vdocuments.us/reader033/viewer/2022060117/55852446d8b42aa86c8b5026/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 2x
i yx
2
1 2 1 2
1 2
x xdydx x
2 d u vu uvdx v v
![Page 6: 11X1 T08 06 quotient & reciprocal rules](https://reader033.vdocuments.us/reader033/viewer/2022060117/55852446d8b42aa86c8b5026/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 2x
i yx
2
1 2 1 2
1 2
x xdydx x
2
1 2 2
1 2
x x
x
2 d u vu uvdx v v
![Page 7: 11X1 T08 06 quotient & reciprocal rules](https://reader033.vdocuments.us/reader033/viewer/2022060117/55852446d8b42aa86c8b5026/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 2x
i yx
2
1 2 1 2
1 2
x xdydx x
2
1 2 2
1 2
x x
x
2 d u vu uvdx v v
2
1
1 2x
![Page 8: 11X1 T08 06 quotient & reciprocal rules](https://reader033.vdocuments.us/reader033/viewer/2022060117/55852446d8b42aa86c8b5026/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 2x
i yx
2
1 2 1 2
1 2
x xdydx x
2
1 2 2
1 2
x x
x
2
2
4
xii y
x
2 d u vu uvdx v v
2
1
1 2x
![Page 9: 11X1 T08 06 quotient & reciprocal rules](https://reader033.vdocuments.us/reader033/viewer/2022060117/55852446d8b42aa86c8b5026/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 2x
i yx
2
1 2 1 2
1 2
x xdydx x
2
1 2 2
1 2
x x
x
2
2
4
xii y
x
1 12 22 2
2
14 2 2 4 2
2
4
x x x xdydx x
2 d u vu uvdx v v
2
1
1 2x
![Page 10: 11X1 T08 06 quotient & reciprocal rules](https://reader033.vdocuments.us/reader033/viewer/2022060117/55852446d8b42aa86c8b5026/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 2x
i yx
2
1 2 1 2
1 2
x xdydx x
2
1 2 2
1 2
x x
x
2
2
4
xii y
x
1 12 22 2
2
14 2 2 4 2
2
4
x x x xdydx x
2 d u vu uvdx v v
2
1
1 2x
1 12 2 22 2
2
2 4 2 4
4
x x x
x
![Page 11: 11X1 T08 06 quotient & reciprocal rules](https://reader033.vdocuments.us/reader033/viewer/2022060117/55852446d8b42aa86c8b5026/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 2x
i yx
2
1 2 1 2
1 2
x xdydx x
2
1 2 2
1 2
x x
x
2
2
4
xii y
x
1 12 22 2
2
14 2 2 4 2
2
4
x x x xdydx x
2 d u vu uvdx v v
2
1
1 2x
1 12 2 22 2
2
2 4 2 4
4
x x x
x
12 2 22
2
2 4 4
4
x x x
x
![Page 12: 11X1 T08 06 quotient & reciprocal rules](https://reader033.vdocuments.us/reader033/viewer/2022060117/55852446d8b42aa86c8b5026/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 2x
i yx
2
1 2 1 2
1 2
x xdydx x
2
1 2 2
1 2
x x
x
2
2
4
xii y
x
1 12 22 2
2
14 2 2 4 2
2
4
x x x xdydx x
2 d u vu uvdx v v
2
1
1 2x
1 12 2 22 2
2
2 4 2 4
4
x x x
x
12 2 22
2
2 4 4
4
x x x
x
2 2
8
4 4x x
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4. Reciprocal Rule 2 d k kvdx v v
![Page 14: 11X1 T08 06 quotient & reciprocal rules](https://reader033.vdocuments.us/reader033/viewer/2022060117/55852446d8b42aa86c8b5026/html5/thumbnails/14.jpg)
4. Reciprocal Rule 2 d k kvdx v v
“MINUS the DERIVATIVE on the FUNCTION SQUARED”
![Page 15: 11X1 T08 06 quotient & reciprocal rules](https://reader033.vdocuments.us/reader033/viewer/2022060117/55852446d8b42aa86c8b5026/html5/thumbnails/15.jpg)
4. Reciprocal Rule 2 d k kvdx v v
“MINUS the DERIVATIVE on the FUNCTION SQUARED”
2
1e.g. i y
x
![Page 16: 11X1 T08 06 quotient & reciprocal rules](https://reader033.vdocuments.us/reader033/viewer/2022060117/55852446d8b42aa86c8b5026/html5/thumbnails/16.jpg)
4. Reciprocal Rule 2 d k kvdx v v
“MINUS the DERIVATIVE on the FUNCTION SQUARED”
2
1e.g. i y
x
4
2dy xdx x
![Page 17: 11X1 T08 06 quotient & reciprocal rules](https://reader033.vdocuments.us/reader033/viewer/2022060117/55852446d8b42aa86c8b5026/html5/thumbnails/17.jpg)
4. Reciprocal Rule 2 d k kvdx v v
“MINUS the DERIVATIVE on the FUNCTION SQUARED”
2
1e.g. i y
x
4
2dy xdx x
3
2x
![Page 18: 11X1 T08 06 quotient & reciprocal rules](https://reader033.vdocuments.us/reader033/viewer/2022060117/55852446d8b42aa86c8b5026/html5/thumbnails/18.jpg)
4. Reciprocal Rule 2 d k kvdx v v
“MINUS the DERIVATIVE on the FUNCTION SQUARED”
2
1e.g. i y
x
4
2dy xdx x
3
2x
2
6
4 3ii y
x
![Page 19: 11X1 T08 06 quotient & reciprocal rules](https://reader033.vdocuments.us/reader033/viewer/2022060117/55852446d8b42aa86c8b5026/html5/thumbnails/19.jpg)
4. Reciprocal Rule 2 d k kvdx v v
“MINUS the DERIVATIVE on the FUNCTION SQUARED”
2
1e.g. i y
x
4
2dy xdx x
3
2x
2
6
4 3ii y
x
22
6 8
4 3
xdydx x
![Page 20: 11X1 T08 06 quotient & reciprocal rules](https://reader033.vdocuments.us/reader033/viewer/2022060117/55852446d8b42aa86c8b5026/html5/thumbnails/20.jpg)
4. Reciprocal Rule 2 d k kvdx v v
“MINUS the DERIVATIVE on the FUNCTION SQUARED”
2
1e.g. i y
x
4
2dy xdx x
3
2x
2
6
4 3ii y
x
22
6 8
4 3
xdydx x
22
48
4 3
x
x
![Page 21: 11X1 T08 06 quotient & reciprocal rules](https://reader033.vdocuments.us/reader033/viewer/2022060117/55852446d8b42aa86c8b5026/html5/thumbnails/21.jpg)
4. Reciprocal Rule 2 d k kvdx v v
“MINUS the DERIVATIVE on the FUNCTION SQUARED”
2
1e.g. i y
x
4
2dy xdx x
3
2x
2
6
4 3ii y
x
22
6 8
4 3
xdydx x
22
48
4 3
x
x
Exercise 7G; 1aceg, 2, 4a, 6a, 8a