3. Calculus Rules
d
2. Product Rule uv uv vu
dx
“Write down the FIRST and DIFF the SECOND, PLUS write down the
SECOND and DIFF the FIRST”
4. Calculus Rulesd
2. Product Rule uv uv vu
dx
“Write down the FIRST and DIFF the SECOND, PLUS write down the
SECOND and DIFF the FIRST”
e.g. i y x 7 x 9 6
5. Calculus Rules
d
2. Product Rule uv uv vu
dx
“Write down the FIRST and DIFF the SECOND, PLUS write down the
SECOND and DIFF the FIRST”
e.g. i y x 7 x 9 6
x 7 9 x8 x 9 6 7 x 6
dy
dx
6. Calculus Rules
d
2. Product Rule uv uv vu
dx
“Write down the FIRST and DIFF the SECOND, PLUS write down the
SECOND and DIFF the FIRST”
e.g. i y x 7 x 9 6
x 7 9 x8 x 9 6 7 x 6
dy
dx
9 x15 7 x15 42 x 6
7. Calculus Rules
d
2. Product Rule uv uv vu
dx
“Write down the FIRST and DIFF the SECOND, PLUS write down the
SECOND and DIFF the FIRST”
e.g. i y x 7 x 9 6
x 7 9 x8 x 9 6 7 x 6
dy
dx
9 x15 7 x15 42 x 6
16 x15 42 x 6
8. Calculus Rules
d
2. Product Rule uv uv vu
dx
“Write down the FIRST and DIFF the SECOND, PLUS write down the
SECOND and DIFF the FIRST”
e.g. i y x 7 x 9 6 ii y x 2 2 x 3
x 7 9 x8 x 9 6 7 x 6
dy
dx
9 x15 7 x15 42 x 6
16 x15 42 x 6
9. Calculus Rules
d
2. Product Rule uv uv vu
dx
“Write down the FIRST and DIFF the SECOND, PLUS write down the
SECOND and DIFF the FIRST”
e.g. i y x 7 x 9 6 ii y x 2 2 x 3
dy
x 9 x x 6 7 x x 2 2 2 x 31
dy 7 8 9 6
dx dx
9 x15 7 x15 42 x 6
16 x15 42 x 6
10. Calculus Rules
d
2. Product Rule uv uv vu
dx
“Write down the FIRST and DIFF the SECOND, PLUS write down the
SECOND and DIFF the FIRST”
e.g. i y x 7 x 9 6 ii y x 2 2 x 3
dy
x 9 x x 6 7 x x 2 2 2 x 31
dy 7 8 9 6
dx dx
9 x15 7 x15 42 x 6 2x 4 2x 3
16 x15 42 x 6
11. Calculus Rules
d
2. Product Rule uv uv vu
dx
“Write down the FIRST and DIFF the SECOND, PLUS write down the
SECOND and DIFF the FIRST”
e.g. i y x 7 x 9 6 ii y x 2 2 x 3
dy
x 9 x x 6 7 x x 2 2 2 x 31
dy 7 8 9 6
dx dx
9 x15 7 x15 42 x 6 2x 4 2x 3
16 x15 42 x 6 4x 7
12. Calculus Rules
d
2. Product Rule uv uv vu
dx
“Write down the FIRST and DIFF the SECOND, PLUS write down the
SECOND and DIFF the FIRST”
e.g. i y x 7 x 9 6 ii y x 2 2 x 3
dy
x 9 x x 6 7 x x 2 2 2 x 31
dy 7 8 9 6
dx dx
9 x15 7 x15 42 x 6 2x 4 2x 3
16 x15 42 x 6 4x 7
iii
d
dx
x 7 x 3 3 x 2 7
13. Calculus Rules
d
2. Product Rule uv uv vu
dx
“Write down the FIRST and DIFF the SECOND, PLUS write down the
SECOND and DIFF the FIRST”
e.g. i y x 7 x 9 6 ii y x 2 2 x 3
dy
x 9 x x 6 7 x x 2 2 2 x 31
dy 7 8 9 6
dx dx
9 x15 7 x15 42 x 6 2x 4 2x 3
16 x15 42 x 6 4x 7
iii
d
dx
x 7 x 3 3 x 2 7
x 7 x 3 6 x 3 x 2 7 7 x 6 3 x 2
14. Calculus Rules
d
2. Product Rule uv uv vu
dx
“Write down the FIRST and DIFF the SECOND, PLUS write down the
SECOND and DIFF the FIRST”
e.g. i y x 7 x 9 6 ii y x 2 2 x 3
dy
x 9 x x 6 7 x x 2 2 2 x 31
dy 7 8 9 6
dx dx
9 x15 7 x15 42 x 6 2x 4 2x 3
16 x15 42 x 6 4x 7
iii
d
dx
x 7 x 3 3 x 2 7
x 7 x 3 6 x 3 x 2 7 7 x 6 3 x 2
6 x8 6 x 4 21x8 9 x 4 49 x 6 21x 2
15. Calculus Rules
d
2. Product Rule uv uv vu
dx
“Write down the FIRST and DIFF the SECOND, PLUS write down the
SECOND and DIFF the FIRST”
e.g. i y x 7 x 9 6 ii y x 2 2 x 3
dy
x 9 x x 6 7 x x 2 2 2 x 31
dy 7 8 9 6
dx dx
9 x15 7 x15 42 x 6 2x 4 2x 3
16 x15 42 x 6 4x 7
iii
d
dx
x 7 x 3 3 x 2 7
x 7 x 3 6 x 3 x 2 7 7 x 6 3 x 2
6 x8 6 x 4 21x8 9 x 4 49 x 6 21x 2
27 x8 49 x 6 15 x 4 21x 2