Test: Differentiation II - Challenging

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Question 1:   Find a derivative of the function   y=arctg(ln( x 2 ))
y'= 2x 1+(ln( x 2 ))
y'= 2 1+(ln( x 2 )) x
y'= 2 1+(ln( x 2 ))
y'= 1 1+(ln( x 2 ))
Question 2:   Find a derivative of a function    y= sin 2 (cos(x))
y'=2sin(cos(x))
y'=sin(2cos(x))
y'=sin(x)sin(2cos(x))
y'=sin(x)sin(2cos(x))
Question 3:   Find a derivative of a function   y= e cos( x 2 )
y'=2x e cos( x 2 )
y'=2x e cos( x 2 ) sin( x 2 )
y'= e cos( x 2 )
y'= e cos( x 2 ) sin( x 2 )
Question 4:   What is the equation of the tangent to the function   y= x 2 +7x1   at a point   x 0 =1
y=9x9
y=9x2
y=9x
y=9x+2
Question 5:   What is the equation of the tangent to the function   y= x 3 + x 2 +1   at the point   x 0 =3
y=33x62
y=33x+37
y=33x
y=33x99
Question 6:   The Newton's first law of motion is expressed by the formula   s(t)= t 3 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 =1
v=5
v=10
v=4
v=1
Question 7:   The Newton's first law of motion is expressed by the formula   s(t)= t 20 t 15 + t 10 +20t  ,  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
v=20
v=15
v=10
v=19
Question 8:   Find the amount of the critical points to the graph   f'(x)   for the segment   [1.5;1)

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

1;+
5;1
;5
;5 1;+
Question 10:   Find range when function   f(x)   is descending, the graph represents   f'(x)

;1
[1;1]
1;+
;+