Test:
Differentiation I - Challenging
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Question 1:
Find a derivative of the function
y
=
1
sin
2
5
x
A
y
'
=
−
10
sin
−
2
5
x
cos
5
x
B
y
'
=
−
10
cos
(
5
x
)
C
y
'
=
−
2
sin
−
3
5
x
D
y
'
=
−
10
sin
−
3
5
x
cos
5
x
Question 2:
Find a derivative of the function
y
=
ln
(
x
cos
(
x
)
)
A
y
'
=
−
t
g
(
x
)
B
y
'
=
1
x
−
t
g
(
x
)
C
y
'
=
cos
(
x
)
−
x
x
cos
(
x
)
D
y
'
=
1
x
cos
(
x
)
Question 3:
Find a derivative of the function
y
=
t
g
(
e
x
10
)
A
y
'
=
e
x
10
cos
2
e
x
10
B
y
'
=
10
x
9
cos
2
e
x
10
C
y
'
=
e
x
10
×
10
x
9
cos
2
e
x
10
D
y
'
=
e
x
10
×
10
x
9
cos
2
e
x
Question 4:
What is the equation of the tangent to the function
y
=
x
2
−
x
+
5
, at the point
x
0
=
2
A
y
=
3
x
−
6
B
y
=
3
x
C
y
=
3
x
−
1
D
y
=
3
x
+
1
Question 5:
What is the equation of the tangent of the function
y
=
x
4
−
3
x
3
+
x
, at the point
x
0
=
1
A
y
=
−
4
x
B
y
=
−
4
x
−
1
C
y
=
−
4
x
+
4
D
y
=
−
4
x
+
3
Question 6:
The Newton's first law of motion is expressed by the formula
s
(
t
)
=
t
7
+
5
t
2
+
sin
(
x
)
, 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
=
0
A
v
=
10
B
v
=
0
C
v
=
1
D
v
=
15
Question 7:
The Newton's first law of motion is expressed by the formula
s
(
t
)
=
t
5
−
7
t
3
, 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
=
4
B
v
=
1
C
v
=
2
D
v
=
−
4
Question 8:
How many critical points are in the graph
f
'
(
x
)
in the range
(
−
1
;
2
)
?
A
5
B
4
C
3
D
2
Question 9:
Find range when function
f
(
x
)
is ascending, the graph represents
f
'
(
x
)
A
−
3
;
−
2
B
−
2
;
+
∞
C
−
∞
;
−
3
D
−
∞
;
−
3
∪
−
2
;
+
∞
Question 10:
Find range when function
f
(
x
)
is descending, the graph represents
f
'
(
x
)
A
−
4
;
0
B
−
∞
;
−
4
C
−
∞
;
+
∞
D
[
−
4
;
−
1.5
]
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