11x1 t08 05 product rule

Calculus Rules

Calculus Rules2. Product Rule

duv uv vu

dx

Calculus Rules2. Product Rule

“Write down the FIRST and DIFF the SECOND, PLUS write down the SECOND and DIFF the FIRST”

duv uv vu

dx

Calculus Rules2. Product Rule

“Write down the FIRST and DIFF the SECOND, PLUS write down the SECOND and DIFF the FIRST”

7 9e.g. 6i y x x

duv uv vu

dx

Calculus Rules2. Product Rule

“Write down the FIRST and DIFF the SECOND, PLUS write down the SECOND and DIFF the FIRST”

7 9e.g. 6i y x x

7 8 9 69 6 7dy

x x x xdx

duv uv vu

dx

Calculus Rules2. Product Rule

“Write down the FIRST and DIFF the SECOND, PLUS write down the SECOND and DIFF the FIRST”

7 9e.g. 6i y x x

7 8 9 69 6 7dy

x x x xdx

15 15 69 7 42x x x

duv uv vu

dx

Calculus Rules2. Product Rule

“Write down the FIRST and DIFF the SECOND, PLUS write down the SECOND and DIFF the FIRST”

7 9e.g. 6i y x x

7 8 9 69 6 7dy

x x x xdx

15 15 69 7 42x x x

duv uv vu

dx

15 616 42x x

Calculus Rules2. Product Rule

“Write down the FIRST and DIFF the SECOND, PLUS write down the SECOND and DIFF the FIRST”

7 9e.g. 6i y x x

7 8 9 69 6 7dy

x x x xdx

15 15 69 7 42x x x

2 2 3ii y x x

duv uv vu

dx

15 616 42x x

Calculus Rules2. Product Rule

“Write down the FIRST and DIFF the SECOND, PLUS write down the SECOND and DIFF the FIRST”

7 9e.g. 6i y x x

7 8 9 69 6 7dy

x x x xdx

15 15 69 7 42x x x

2 2 3ii y x x

2 2 2 3 1dy

x xdx

duv uv vu

dx

15 616 42x x

Calculus Rules2. Product Rule

“Write down the FIRST and DIFF the SECOND, PLUS write down the SECOND and DIFF the FIRST”

7 9e.g. 6i y x x

7 8 9 69 6 7dy

x x x xdx

15 15 69 7 42x x x

2 2 3ii y x x

2 2 2 3 1dy

x xdx

2 4 2 3x x

duv uv vu

dx

15 616 42x x

Calculus Rules2. Product Rule

“Write down the FIRST and DIFF the SECOND, PLUS write down the SECOND and DIFF the FIRST”

7 9e.g. 6i y x x

7 8 9 69 6 7dy

x x x xdx

15 15 69 7 42x x x

2 2 3ii y x x

2 2 2 3 1dy

x xdx

2 4 2 3x x

duv uv vu

dx

15 616 42x x 4 7x

Calculus Rules2. Product Rule

“Write down the FIRST and DIFF the SECOND, PLUS write down the SECOND and DIFF the FIRST”

7 9e.g. 6i y x x

7 8 9 69 6 7dy

x x x xdx

15 15 69 7 42x x x

2 2 3ii y x x

2 2 2 3 1dy

x xdx

2 4 2 3x x

7 3 2 3 7d

iii x x xdx

duv uv vu

dx

15 616 42x x 4 7x

Calculus Rules2. Product Rule

“Write down the FIRST and DIFF the SECOND, PLUS write down the SECOND and DIFF the FIRST”

7 9e.g. 6i y x x

7 8 9 69 6 7dy

x x x xdx

15 15 69 7 42x x x

2 2 3ii y x x

2 2 2 3 1dy

x xdx

2 4 2 3x x

7 3 2 3 7d

iii x x xdx

7 3 2 6 26 3 7 7 3x x x x x x

duv uv vu

dx

15 616 42x x 4 7x

Calculus Rules2. Product Rule

“Write down the FIRST and DIFF the SECOND, PLUS write down the SECOND and DIFF the FIRST”

7 9e.g. 6i y x x

7 8 9 69 6 7dy

x x x xdx

15 15 69 7 42x x x

2 2 3ii y x x

2 2 2 3 1dy

x xdx

2 4 2 3x x

7 3 2 3 7d

iii x x xdx

7 3 2 6 26 3 7 7 3x x x x x x 8 4 8 4 6 26 6 21 9 49 21x x x x x x

duv uv vu

dx

15 616 42x x 4 7x

Calculus Rules2. Product Rule

“Write down the FIRST and DIFF the SECOND, PLUS write down the SECOND and DIFF the FIRST”

7 9e.g. 6i y x x

7 8 9 69 6 7dy

x x x xdx

15 15 69 7 42x x x

2 2 3ii y x x

2 2 2 3 1dy

x xdx

2 4 2 3x x

7 3 2 3 7d

iii x x xdx

7 3 2 6 26 3 7 7 3x x x x x x 8 4 8 4 6 26 6 21 9 49 21x x x x x x

duv uv vu

dx

15 616 42x x 4 7x

8 6 4 227 49 15 21x x x x

52 3 4iv y x x

4 52 23 5 4 2 4 3dy

x x x xdx

52 3 4iv y x x

4 52 23 5 4 2 4 3dy

x x x xdx

52 3 4iv y x x

4 52 2 230 4 3 4x x x

4 52 23 5 4 2 4 3dy

x x x xdx

52 3 4iv y x x

4 52 2 230 4 3 4x x x

42 2 24 30 3 4x x x

4 52 23 5 4 2 4 3dy

x x x xdx

52 3 4iv y x x

4 52 2 230 4 3 4x x x

42 2 24 30 3 4x x x

42 24 33 12x x

4 52 23 5 4 2 4 3dy

x x x xdx

52 3 4iv y x x

4 52 2 230 4 3 4x x x

42 2 24 30 3 4x x x

42 24 33 12x x

42 23 4 11 4x x

4 52 23 5 4 2 4 3dy

x x x xdx

52 3 4iv y x x

2 2 1v y x x

4 52 2 230 4 3 4x x x

42 2 24 30 3 4x x x

42 24 33 12x x

42 23 4 11 4x x

4 52 23 5 4 2 4 3dy

x x x xdx

52 3 4iv y x x

2 2 1v y x x

4 52 2 230 4 3 4x x x

42 2 24 30 3 4x x x

42 24 33 12x x

42 23 4 11 4x x

122 2 1x x

4 52 23 5 4 2 4 3dy

x x x xdx

52 3 4iv y x x

2 2 1v y x x

1 12 2

12 2 1 2 2 1 2

2dy

x x xdx

4 52 2 230 4 3 4x x x

42 2 24 30 3 4x x x

42 24 33 12x x

42 23 4 11 4x x

122 2 1x x

4 52 23 5 4 2 4 3dy

x x x xdx

52 3 4iv y x x

2 2 1v y x x

1 12 2

12 2 1 2 2 1 2

2dy

x x xdx

4 52 2 230 4 3 4x x x

42 2 24 30 3 4x x x

42 24 33 12x x

42 23 4 11 4x x

122 2 1x x

1 12 22 2 1 2 2 1x x x

4 52 23 5 4 2 4 3dy

x x x xdx

52 3 4iv y x x

2 2 1v y x x

1 12 2

12 2 1 2 2 1 2

2dy

x x xdx

4 52 2 230 4 3 4x x x

42 2 24 30 3 4x x x

42 24 33 12x x

42 23 4 11 4x x

122 2 1x x

1 12 22 2 1 2 2 1x x x

122 2 1 2 1x x x

4 52 23 5 4 2 4 3dy

x x x xdx

52 3 4iv y x x

2 2 1v y x x

1 12 2

12 2 1 2 2 1 2

2dy

x x xdx

4 52 2 230 4 3 4x x x

42 2 24 30 3 4x x x

42 24 33 12x x

42 23 4 11 4x x

122 2 1x x

1 12 22 2 1 2 2 1x x x

122 2 1 2 1x x x

122 2 1 3 1x x

4 52 23 5 4 2 4 3dy

x x x xdx

52 3 4iv y x x

2 2 1v y x x

1 12 2

12 2 1 2 2 1 2

2dy

x x xdx

4 52 2 230 4 3 4x x x

42 2 24 30 3 4x x x

42 24 33 12x x

42 23 4 11 4x x

122 2 1x x

1 12 22 2 1 2 2 1x x x

122 2 1 2 1x x x

122 2 1 3 1x x

2 3 1

2 1

xdydx x

4 52 23 5 4 2 4 3dy

x x x xdx

52 3 4iv y x x

2 2 1v y x x

1 12 2

12 2 1 2 2 1 2

2dy

x x xdx

Exercise 7F; 1ac, 2bdf,3a, 4ad, 5, 6ac,

7, 9, 13a*

4 52 2 230 4 3 4x x x

42 2 24 30 3 4x x x

42 24 33 12x x

42 23 4 11 4x x

122 2 1x x

1 12 22 2 1 2 2 1x x x

122 2 1 2 1x x x

122 2 1 3 1x x

2 3 1

2 1

xdydx x