Calculus Rules
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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 2xi y
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 2xi y
x
2
1 2 1 21 2x xdy
dx 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 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
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
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
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
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
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
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
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”
21e.g. i yx
4. Reciprocal Rule 2 d k kvdx v v
“MINUS the DERIVATIVE on the FUNCTION SQUARED”
21e.g. i yx
42dy x
dx x
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
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
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
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
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
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