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Solved Examples
Curriculum:
Iowa Math Framework
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Topic:
Computation of Derivatives
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Lesson:
The Product and Quotient Rules
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Attempt following question by selecting a choice to answer.
e
Find
D
x
(
7
x
+
x
1
-
x
)
.
eee eee
A.
e
1
4
x
-
x
+
1
x
(
1
-
x
)
2
B.
e
1
4
x
+
x
+
1
2
x
(
1
-
x
)
2
C.
e
x
+
x
+
1
2
x
(
1
-
x
)
2
D.
e
1
4
x
2
x
(
1
-
x
)
2
ee
B
View Solution Steps
Step 1: D
x
=
7
x
+
x
1
2
1
-
x
Step 2:
(
1
-
x
)
[
7
+
1
2
x
-
1
2
]
-
(
7
x
+
x
1
2
)
(
-
1
)
(
1
-
x
)
2
[Use the quotient rule.]
Step 3: =
(
1
-
x
)
[
7
+
1
2
x
1
2
]
+
(
7
x
+
x
1
2
)
(
1
-
x
)
2
Step 4: =
(
1
-
x
)
[
1
4
x
1
2
+
1
2
x
1
2
]
+
(
7
x
+
x
1
2
)
(
1
-
x
)
2
Step 5: =
(
1
-
x
)
(
1
4
x
1
2
+
1
)
+
2
x
1
2
(
7
x
+
x
1
2
)
2
x
1
2
(
1
4
-
x
)
2
Step 6: =
1
4
x
1
2
+
1
-
1
4
x
3
2
-
x
+
1
4
x
3
2
+
2
x
2
x
1
2
(
1
-
x
)
2
Step 7: =
1
4
x
1
2
+
x
+
1
2
x
1
2
(
1
-
x
)
2
=
1
4
x
+
x
+
1
2
x
(
1
-
x
)
2
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