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