4 Group 10
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Question 1.
The derivative of function
f
(
x
)
=
(
1
+
ln
1
x
)
5
is
a)
f
′
(
x
)
=
5
x
(
1
+
ln
1
x
)
4
b)
f
′
(
x
)
=
-
5
x
(
1
+
ln
1
x
)
4
c)
f
′
(
x
)
=
1
4
x
(
1
+
ln
1
x
)
4
d)
f
′
(
x
)
=
-
1
6
x
(
1
+
ln
1
x
)
6
e)
f
′
(
x
)
=
-
1
x
(
1
+
ln
1
x
)
4
Question 2.
The equation of the tangent line to the graph of function
f
(
x
)
=
arctg
x
at point
[
-
1
,
?
]
is
a)
4
x
-
4
y
+
4
-
π
=
0
b)
x
-
2
y
+
1
-
π
=
0
c)
8
x
-
4
y
+
8
-
π
=
0
d)
2
x
-
4
y
+
2
-
π
=
0
e)
2
x
-
4
y
+
2
+
π
=
0
Question 3.
The function
f
(
x
)
=
e
x
(
x
-
1
)
+
2
is increasing on the interval
a)
⟨
-
2
,
2
⟩
b)
⟨
-
1
,
2
⟩
c)
⟨
1
,
2
⟩
d)
⟨
-
2
,
0
⟩
e)
⟨
-
1
,
1
⟩
Evaluate