Test: Differentiation III - Ambitious

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Question 1:   Find a derivative of the function   y=ln( x 3 +7 x 2 )
y'= 3 x 2 +14 x 3 +7 x 2
y'= 1 x 3 +7 x 2
y'= 3 x 2 x 3 +7 x 2
y'=3 x 2 +14
Question 2:   Find a derivative of the function   y=sin( x 2 )
y'=cos( x 2 )
y'=2x
y'=2xcos( x 2 )
y'=2xcos( x 2 )
Question 3:   Find a derivative of the function   y=arccos(5x)
y'= 1 125 x 2
y'= 5 125 x 2
y'= 1 125 x 2
y'= 5 125 x 2
Question 4:   Find a derivative of the function   y= x 4 x 3
y'= x 3 x 2
y'= x 4 x 3
y'=4 x 3 3 x 2
y'=4 x 3 x 2
Question 5:   The Newton's first law of motion is expressed by the formula   s(t)= t 2 9t  ,  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
v=15
v=21
v=20
v=9
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
v=26
v=12
v=20
v=32
Question 7:   The Newton's first law of motion is expressed by the formula   s(t)= t 3 3t  ,  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
v=3
v=1
v=5
v=0
Question 8:   In which point   f'( x 0 )>0 ?

x 0 =0.5
x 0 =2.5
x 0 =0
x 0 =0.5
Question 9:   In which point   f'( x 0 )=0 ?

x 0 =1
x 0 =0
x 0 =1
x 0 =2
Question 10:   In which point   f'( x 0 )<0 ?

x 0 =1
x 0 =2
x 0 =0
x 0 =1