Test:
Differentiation III - Challenging
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Question 1:
Find a derivative of the function
y
=
cos
(
ln
(
5
x
)
)
A
y
'
=
−
sin
(
ln
5
x
)
B
y
'
=
−
sin
(
ln
5
x
)
x
C
y
'
=
−
5
sin
(
ln
5
x
)
x
D
y
'
=
−
sin
(
ln
5
x
)
5
x
Question 2:
Find a derivative of the function
y
=
5
cos
(
x
)
A
y
'
=
−
sin
(
x
)
5
cos
(
x
)
B
y
'
=
ln
(
5
)
5
cos
(
x
)
C
y
'
=
−
sin
(
x
)
ln
(
5
)
5
cos
(
x
)
D
y
'
=
sin
(
x
)
ln
(
5
)
5
cos
(
x
)
Question 3:
Find a derivative of the function
y
=
log
2
(
x
2
)
A
y
'
=
1
x
ln
(
2
)
B
y
'
=
2
x
ln
(
2
)
C
y
'
=
2
x
ln
(
2
)
D
y
'
=
2
x
Question 4:
What is the equation of the tangent to the function
y
=
x
3
−
4
x
−
1
, at the point
x
0
=
2
A
y
=
8
x
B
y
=
8
x
−
1
C
y
=
8
x
−
16
D
y
=
8
x
−
17
Question 5:
What is the equation of the tangent to the function
y
=
x
2
−
x
+
1
, at the point
x
0
=
0
A
y
=
x
−
1
B
y
=
−
x
+
2
C
y
=
−
x
D
y
=
−
x
+
1
Question 6:
The Newton's first law of motion is expressed by the formula
s
(
t
)
=
t
2
−
5
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
=
3
.
A
v
=
3
B
v
=
2
C
v
=
1
D
v
=
4
Question 7:
The Newton's first law of motion is expressed by the formula
s
(
t
)
=
ln
(
t
)
+
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
=
2
.
A
v
=
2
B
v
=
1.5
C
v
=
1
D
v
=
2.5
Question 8:
What is the amount of the critical point to the graph
f
'
(
x
)
in the range
−
2
;
1
A
4
B
2
C
3
D
1
Question 9:
Find range when function
f
(
x
)
is ascending, the graph represents
f
'
(
x
)
A
0
;
3
B
3
;
+
∞
C
−
∞
;
+
∞
D
−
∞
;
3
Question 10:
Find range when function
f
(
x
)
is descending, the graph represents
f
'
(
x
)
A
0
;
1.3
B
−
∞
;
−
1
C
[
−
1
;
1.3
]
D
−
∞
;
−
1
∪
0
;
1.3
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