Test: Differentiation III - Challenging

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Question 1:   Find a derivative of the function   y=cos(ln(5x))
y'= sin(ln 5x ) x
y'= 5sin(ln 5x ) x
y'=sin(ln 5x )
y'= sin(ln 5x ) 5x
Question 2:   Find a derivative of the function   y= 5 cos(x)
y'=sin(x) 5 cos(x)
y'=sin(x)ln(5) 5 cos(x)
y'=ln(5) 5 cos(x)
y'=sin(x)ln(5) 5 cos(x)
Question 3:   Find a derivative of the function   y= log 2 ( x 2 )
y'= 2x ln(2)
y'= 2 xln(2)
y'= 1 xln(2)
y'= 2 x
Question 4:   What is the equation of the tangent to the function   y= x 3 4x1  ,  at the point   x 0 =2
y=8x17
y=8x1
y=8x16
y=8x
Question 5:   What is the equation of the tangent to the function   y= x 2 x+1  ,  at the point   x 0 =0
y=x1
y=x+2
y=x
y=x+1
Question 6:   The Newton's first law of motion is expressed by the formula   s(t)= t 2 5t  ,  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 .
v=4
v=1
v=2
v=3
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 .
v=2
v=1.5
v=1
v=2.5
Question 8:   What is the amount of the critical point to the graph   f'(x)   in the range   2;1

4
3
2
1
Question 9:   Find range when function   f(x)   is ascending, the graph represents   f'(x)

3;+
;+
0;3
;3
Question 10:   Find range when function   f(x)   is descending, the graph represents   f'(x)

;1
0;1.3
;1 0;1.3
[1;1.3]