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Solved Examples
Curriculum:
Alaska Math Grade Level Expectations
Click to change Curriculum
Topic:
Differentiation
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Lesson:
Product, Quotient, and Chain Rules
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Attempt following question by selecting a choice to answer.
D
If
m
=
v
(
9
v
2
+
1
0
v
-
1
1
)
,
then find
d
m
d
v
.
ee DD
A.
D
9
v
2
+
1
0
v
-
1
1
+
2
v
(
1
8
v
+
1
0
)
2
v
B.
D
4
5
v
2
+
3
0
v
-
1
1
2
v
C.
D
4
5
v
2
+
1
0
v
-
1
1
2
v
D.
D
Does not exist
E.
D
2
7
v
2
+
2
0
v
-
1
1
v
D
B
View Solution Steps
Step 1:
m
=
v
(
9
v
2
+
1
0
v
-
1
1
)
[Write the function.]
Step 2:
d
m
d
v
=
d
d
v
v
(
9
v
2
+
1
0
v
-
1
1
)
[Find
d
m
d
v
.]
Step 3: =
v
d
d
v
(
9
v
2
+
1
0
v
-
1
1
)
+
(
9
v
2
+
1
0
v
-
1
1
)
d
d
v
v
[Use the Product Rule.]
Step 4: =
v
(
1
8
v
+
1
0
)
+
(
9
v
2
+
1
0
v
-
1
1
)
(
1
2
v
)
Step 5: = (18
v
+ 10)
v
+
9
v
2
+
1
0
v
-
1
1
2
v
Step 6: =
4
5
v
2
+
3
0
v
-
1
1
2
v
[Simplify.]
Step 7:
d
m
d
v
=
4
5
v
2
+
3
0
v
-
1
1
2
v
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