11x1 t08 06 quotient & reciprocal rules
TRANSCRIPT
Calculus Rules
Calculus Rules3. Quotient Rule
2 d u vu uvdx v v
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
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
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
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
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
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
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
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
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
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
4. Reciprocal Rule 2 d k kvdx v v
4. Reciprocal Rule 2 d k kvdx v v
“MINUS the DERIVATIVE on the FUNCTION SQUARED”
4. Reciprocal Rule 2 d k kvdx v v
“MINUS the DERIVATIVE on the FUNCTION SQUARED”
2
1e.g. i y
x
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
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
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
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
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
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