Test:
Differentiation II - Ambitious
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Question 1:
Find a derivative of the function
y
=
e
(
x
7
+
3
x
2
)
A
y
'
=
(
7
x
6
+
6
x
)
e
(
x
7
+
3
x
2
)
B
y
'
=
e
(
x
7
+
3
x
2
)
C
y
'
=
(
x
7
+
3
x
2
)
e
(
x
7
+
3
x
2
)
D
y
'
=
(
x
6
+
3
x
)
e
(
x
7
+
3
x
2
)
Question 2:
Find a derivative of the function
y
=
(
x
−
2
)
2
A
y
'
=
6
(
3
x
−
2
)
B
y
'
=
3
x
−
2
C
y
'
=
2
(
3
x
−
2
)
D
y
'
=
6
(
x
−
2
)
Question 3:
Find a derivative of the function
y
=
a
r
c
t
g
(
3
x
)
A
y
'
=
3
1
+
3
x
B
y
'
=
3
1
+
9
x
2
C
y
'
=
−
3
1
+
9
x
2
D
y
'
=
1
1
+
9
x
2
Question 4:
Find a derivative of the function
y
=
t
g
(
x
5
−
x
)
A
y
'
=
5
x
4
−
1
cos
2
(
x
5
)
B
y
'
=
1
cos
2
(
x
5
−
x
)
C
y
'
=
5
x
4
cos
2
(
x
5
−
x
)
D
y
'
=
5
x
4
−
1
cos
2
(
x
5
−
x
)
Question 5:
The Newton's first law of motion is expressed by the formula
s
(
t
)
=
t
3
−
7
, where
t
- time (in seconds),
s
(
t
)
- deviation of a point in the moment of time
t
(in meters) from the initial position. Find the speed of movement at the point
t
0
=
2
A
v
=
5
B
v
=
12
C
v
=
10
D
v
=
1
Question 6:
The Newton's first law of motion is expressed by the formula
s
(
t
)
=
t
2
+
4
t
, where
t
- time (in seconds),
s
(
t
)
- deviation of a point in the moment of time
t
(in meters) from the initial position. Find the speed of movement at the point
t
0
=
1
.
A
v
=
4
B
v
=
5
C
v
=
6
D
v
=
9
Question 7:
The Newton's first law of motion is expressed by the formula
s
(
t
)
=
t
4
−
2
t
2
, where
t
- time (in seconds),
s
(
t
)
- deviation of a point in the moment of time
t
(in meters) from the initial position. Find the speed of movement at the point
t
0
=
3
.
A
v
=
6
B
v
=
108
C
v
=
27
D
v
=
81
Question 8:
In which point
f
'
(
x
0
)
>
0
?
A
x
0
=
4
B
x
0
=
6
C
x
0
=
10
D
x
0
=
8
Question 9:
In which point
f
'
(
x
0
)
=
0
?
A
x
0
=
0
B
x
0
=
−
2
C
x
0
=
1
D
x
0
=
−
1
Question 10:
In which point
f
'
(
x
0
)
<
0
?
A
x
0
=
1
B
x
0
=
3
C
x
0
=
0
D
x
0
=
−
2
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