Test:
Differentiation III - Ambitious
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Question 1:
Find a derivative of the function
y
=
ln
(
x
3
+
7
x
2
)
A
y
'
=
3
x
2
x
3
+
7
x
2
B
y
'
=
3
x
2
+
14
x
3
+
7
x
2
C
y
'
=
3
x
2
+
14
D
y
'
=
1
x
3
+
7
x
2
Question 2:
Find a derivative of the function
y
=
sin
(
x
2
)
A
y
'
=
2
x
cos
(
x
2
)
B
y
'
=
−
2
x
cos
(
x
2
)
C
y
'
=
2
x
D
y
'
=
cos
(
x
2
)
Question 3:
Find a derivative of the function
y
=
arccos
(
5
x
)
A
y
'
=
−
1
1
−
25
x
2
B
y
'
=
1
1
−
25
x
2
C
y
'
=
5
1
−
25
x
2
D
y
'
=
−
5
1
−
25
x
2
Question 4:
Find a derivative of the function
y
=
x
4
−
x
3
A
y
'
=
x
3
−
x
2
B
y
'
=
4
x
3
−
x
2
C
y
'
=
x
4
−
x
3
D
y
'
=
4
x
3
−
3
x
2
Question 5:
The Newton's first law of motion is expressed by the formula
s
(
t
)
=
t
2
−
9
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
=
15
A
v
=
20
B
v
=
21
C
v
=
9
D
v
=
15
Question 6:
The Newton's first law of motion is expressed by the formula
s
(
t
)
=
t
3
+
20
, 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
=
20
B
v
=
26
C
v
=
12
D
v
=
32
Question 7:
The Newton's first law of motion is expressed by the formula
s
(
t
)
=
t
3
−
3
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
=
5
B
v
=
0
C
v
=
1
D
v
=
3
Question 8:
In which point
f
'
(
x
0
)
>
0
?
A
x
0
=
2.5
B
x
0
=
0.5
C
x
0
=
0
D
x
0
=
−
0.5
Question 9:
In which point
f
'
(
x
0
)
=
0
?
A
x
0
=
−
2
B
x
0
=
0
C
x
0
=
1
D
x
0
=
−
1
Question 10:
In which point
f
'
(
x
0
)
<
0
?
A
x
0
=
1
B
x
0
=
0
C
x
0
=
−
1
D
x
0
=
2
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