Calculus Rules
11X1 T09 05 product rule (2010)
Jul 08, 2015
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Calculus Rules
Calculus Rules2. Product Rule d uv uv vu
dx
Calculus Rules2. Product Rule
“Write down the FIRST and DIFF the SECOND, PLUS write down the SECOND and DIFF the FIRST”
d uv uv vudx
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
d uv uv vudx
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
d uv uv vudx
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
d uv uv vudx
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
d uv uv vudx
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
d uv uv vudx
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
d uv uv vudx
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
d uv uv vudx
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
d uv uv vudx
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 7diii x x xdx
d uv uv vudx
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 7diii x x xdx
7 3 2 6 26 3 7 7 3x x x x x x
d uv uv vudx
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 7diii 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
d uv uv vudx
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 7diii 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
d uv uv vudx
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 22
dy 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 22
dy 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 22
dy 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 22
dy 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 22
dy 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 12 1xdy
dx 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 22
dy 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 12 1xdy
dx x
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