Question 1:   Find a derivative of the function  $y=arctg(\ln (x^2))$

Question 2:   Find a derivative of a function   $y={\sin }^2(\cos (x))$

Question 3:   Find a derivative of a function  $y=e^{\cos (x^2)}$

Question 4:   What is the equation of the tangent to the function  $y=x^2+7x-1$  at a point  $x_0=1$

Question 5:   What is the equation of the tangent to the function  $y=x^3+x^2+1$  at the point  $x_0=3$

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  $t_0=1$

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  $t_0=0$

Question 8:   Find the amount of the critical points to the graph  $f\text{'}(x)$  for the segment  $[-1.5;1)$

Question 9:   Find range when function  $f(x)$  is ascending, the graph represents  $f\text{'}(x)$

Question 10:   Find range when function  $f(x)$  is descending, the graph represents  $f\text{'}(x)$