3. Calculus Rules
2. Product Rule
“Write down the FIRST and DIFF the SECOND, PLUS write down the
SECOND and DIFF the FIRST”
d
uv uv vu
dx
4. Calculus Rules
2. Product Rule
“Write down the FIRST and DIFF the SECOND, PLUS write down the
SECOND and DIFF the FIRST”
7 9
e.g. 6i y x x
d
uv uv vu
dx
5. Calculus Rules
2. Product Rule
“Write down the FIRST and DIFF the SECOND, PLUS write down the
SECOND and DIFF the FIRST”
7 9
e.g. 6i y x x
7 8 9 6
9 6 7
dy
x x x x
dx
d
uv uv vu
dx
6. Calculus Rules
2. Product Rule
“Write down the FIRST and DIFF the SECOND, PLUS write down the
SECOND and DIFF the FIRST”
7 9
e.g. 6i y x x
7 8 9 6
9 6 7
dy
x x x x
dx
15 15 6
9 7 42x x x
d
uv uv vu
dx
7. Calculus Rules
2. Product Rule
“Write down the FIRST and DIFF the SECOND, PLUS write down the
SECOND and DIFF the FIRST”
7 9
e.g. 6i y x x
7 8 9 6
9 6 7
dy
x x x x
dx
15 15 6
9 7 42x x x
d
uv uv vu
dx
15 6
16 42x x
8. Calculus Rules
2. Product Rule
“Write down the FIRST and DIFF the SECOND, PLUS write down the
SECOND and DIFF the FIRST”
7 9
e.g. 6i y x x
7 8 9 6
9 6 7
dy
x x x x
dx
15 15 6
9 7 42x x x
2 2 3ii y x x
d
uv uv vu
dx
15 6
16 42x x
9. Calculus Rules
2. Product Rule
“Write down the FIRST and DIFF the SECOND, PLUS write down the
SECOND and DIFF the FIRST”
7 9
e.g. 6i y x x
7 8 9 6
9 6 7
dy
x x x x
dx
15 15 6
9 7 42x x x
2 2 3ii y x x
2 2 2 3 1
dy
x x
dx
d
uv uv vu
dx
15 6
16 42x x
10. Calculus Rules
2. Product Rule
“Write down the FIRST and DIFF the SECOND, PLUS write down the
SECOND and DIFF the FIRST”
7 9
e.g. 6i y x x
7 8 9 6
9 6 7
dy
x x x x
dx
15 15 6
9 7 42x x x
2 2 3ii y x x
2 2 2 3 1
dy
x x
dx
2 4 2 3x x
d
uv uv vu
dx
15 6
16 42x x
11. Calculus Rules
2. Product Rule
“Write down the FIRST and DIFF the SECOND, PLUS write down the
SECOND and DIFF the FIRST”
7 9
e.g. 6i y x x
7 8 9 6
9 6 7
dy
x x x x
dx
15 15 6
9 7 42x x x
2 2 3ii y x x
2 2 2 3 1
dy
x x
dx
2 4 2 3x x
d
uv uv vu
dx
15 6
16 42x x 4 7x
12. Calculus Rules
2. Product Rule
“Write down the FIRST and DIFF the SECOND, PLUS write down the
SECOND and DIFF the FIRST”
7 9
e.g. 6i y x x
7 8 9 6
9 6 7
dy
x x x x
dx
15 15 6
9 7 42x x x
2 2 3ii y x x
2 2 2 3 1
dy
x x
dx
2 4 2 3x x
7 3 2
3 7
d
iii x x x
dx
d
uv uv vu
dx
15 6
16 42x x 4 7x
13. Calculus Rules
2. Product Rule
“Write down the FIRST and DIFF the SECOND, PLUS write down the
SECOND and DIFF the FIRST”
7 9
e.g. 6i y x x
7 8 9 6
9 6 7
dy
x x x x
dx
15 15 6
9 7 42x x x
2 2 3ii y x x
2 2 2 3 1
dy
x x
dx
2 4 2 3x x
7 3 2
3 7
d
iii x x x
dx
7 3 2 6 2
6 3 7 7 3x x x x x x
d
uv uv vu
dx
15 6
16 42x x 4 7x
14. Calculus Rules
2. Product Rule
“Write down the FIRST and DIFF the SECOND, PLUS write down the
SECOND and DIFF the FIRST”
7 9
e.g. 6i y x x
7 8 9 6
9 6 7
dy
x x x x
dx
15 15 6
9 7 42x x x
2 2 3ii y x x
2 2 2 3 1
dy
x x
dx
2 4 2 3x x
7 3 2
3 7
d
iii x x x
dx
7 3 2 6 2
6 3 7 7 3x x x x x x
8 4 8 4 6 2
6 6 21 9 49 21x x x x x x
d
uv uv vu
dx
15 6
16 42x x 4 7x
15. Calculus Rules
2. Product Rule
“Write down the FIRST and DIFF the SECOND, PLUS write down the
SECOND and DIFF the FIRST”
7 9
e.g. 6i y x x
7 8 9 6
9 6 7
dy
x x x x
dx
15 15 6
9 7 42x x x
2 2 3ii y x x
2 2 2 3 1
dy
x x
dx
2 4 2 3x x
7 3 2
3 7
d
iii x x x
dx
7 3 2 6 2
6 3 7 7 3x x x x x x
8 4 8 4 6 2
6 6 21 9 49 21x x x x x x
d
uv uv vu
dx
15 6
16 42x x 4 7x
8 6 4 2
27 49 15 21x x x x