29 May Math exam
MATHEMATICAL ANALYSIS III, MATH 183
Exam 2
1. Use the product rule for differentiation to find derivatives in each of the following:
)
(
)
1
x
2
x
3
x
2
x
1
x
f
2
+
÷
ø
ö
ç
è
æ
+
+
=
(
)
3
x
3
x
x
f
2
2
–
+
=
(
)
x
2
4
x
x
f
–
=
(
)
1
x
x
x
x
f
2
2
3
+
+
=
(
)
(
)
2
3
2
x
4
x
f
+
=
(
)
(
)
3
2
/
1
3
/
1
x
3
x
2
x
f
–
+
=
(
)
2
1
2
x
3
x
x
2
x
f
÷
÷
ø
ö
ç
ç
è
æ
+
=
(
)
(
)
x
3
2
e
1
x
x
f
×
–
=
(
)
1
x
ln
x
y
3
2
–
=
x
e
e
y
x
2
x
2
–
=
–
(
)
25
x
x
f
2
–
=
x
2
x
4
x
8
y
3
–
=
(
)
x
8
x
2
x
f
3
–
=
(
)
1
x
3
x
x
f
–
+
=
(
)
x
2
x
4
x
2
x
f
2
3
+
–
=
(
)
2
x
1
x
x
f
–
–
=
(
)
(
)
(
)
x
3
x
4
x
2
x
3
x
x
f
2
3
2
+
+
+
+
=
(
)
(
)
(
)
3
x
2
3
x
x
f
2
–
+
=
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