Test: Differentiation I - Challenging

Double click on maths expressions to zoom
Question 1:   Find a derivative of the function   y= 1 sin 2 5x
y'=2 sin 3 5x
y'=10 sin 2 5x cos 5x
y'=10cos(5x)
y'=10 sin 3 5x cos 5x
Question 2:   Find a derivative of the function   y=ln(xcos(x))
y'= 1 xcos(x)
y'=tg(x)
y'= cos(x)x xcos(x)
y'= 1 x tg(x)
Question 3:   Find a derivative of the function   y=tg( e x 10 )
y'= e x 10 ×10 x 9 cos 2 e x
y'= 10 x 9 cos 2 e x 10
y'= e x 10 cos 2 e x 10
y'= e x 10 ×10 x 9 cos 2 e x 10
Question 4:   What is the equation of the tangent to the function   y= x 2 x+5  ,  at the point   x 0 =2
y=3x
y=3x6
y=3x1
y=3x+1
Question 5:   What is the equation of the tangent of the function   y= x 4 3 x 3 +x   ,  at the point   x 0 =1
y=4x+3
y=4x
y=4x1
y=4x+4
Question 6:   The Newton's first law of motion is expressed by the formula   s(t)= t 7 +5 t 2 +sin(x)  ,  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=15
v=0
v=1
v=10
Question 7:   The Newton's first law of motion is expressed by the formula   s(t)= t 5 7 t 3  ,  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=4
v=1
v=4
Question 8:   How many critical points are in the graph   f'(x)   in the range   (1;2) ?

3
5
2
4
Question 9:   Find range when function   f(x)   is ascending, the graph represents   f'(x)

2;+
3;2
;3 2;+
;3
Question 10:   Find range when function   f(x)   is descending, the graph represents   f'(x)

;+
;4
4;0
[4;1.5]