Test: Differentiation II - Ambitious

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Question 1:   Find a derivative of the function   y= e ( x 7 +3 x 2 )
y'=( x 6 +3x) e ( x 7 +3 x 2 )
y'=( x 7 +3 x 2 ) e ( x 7 +3 x 2 )
y'=(7 x 6 +6x) e ( x 7 +3 x 2 )
y'= e ( x 7 +3 x 2 )
Question 2:   Find a derivative of the function   y= (x2) 2
y'=2(3x2)
y'=6(x2)
y'=6(3x2)
y'=3x2
Question 3:   Find a derivative of the function   y=arctg(3x)
y'= 3 1+3x
y'= 3 1+9 x 2
y'= 1 1+9 x 2
y'= 3 1+9 x 2
Question 4:   Find a derivative of the function   y=tg( x 5 x)
y'= 5 x 4 1 cos 2 ( x 5 x)
y'= 1 cos 2 ( x 5 x)
y'= 5 x 4 cos 2 ( x 5 x)
y'= 5 x 4 1 cos 2 ( x 5 )
Question 5:   The Newton's first law of motion is expressed by the formula   s(t)= t 3 7  ,  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=1
v=12
v=10
v=5
Question 6:   The Newton's first law of motion is expressed by the formula   s(t)= t 2 +4t  ,  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=6
v=4
v=5
v=9
Question 7:   The Newton's first law of motion is expressed by the formula   s(t)= t 4 2 t 2  ,  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=81
v=6
v=27
v=108
Question 8:   In which point f'( x 0 )>0 ?

x 0 =4
x 0 =6
x 0 =10
x 0 =8
Question 9:   In which point f'( x 0 )=0 ?

x 0 =0
x 0 =1
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 =3