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