11X1 T08 06 quotient & reciprocal rules

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