IDZ Ryabushko Option 10 KR "Derivatives and their appli

Test "Derivatives and their applications" (2 hours). 260 pages

1. Find the first derivative of y′

2. Find the first derivative of y′
2.10 y = ex/√3arctg2x

3. Calculate the first derivative of the function for the specified value of the argument or parameter or for the given coordinates of the point.
3.10 f(x) = x3/3 – x2 + x, x = –1

4. Find the second derivative of y′′
4.10 y = ln lnx

5. Find the second derivative d2y/dx2 of the function.

6. Solve the following problems.
6.10. Find the angle of intersection of the lines y = √2sinx and y = √2cosx

7. Solve the following problems.
7.10. The dependence of the path on time during rectilinear motion of a point is given by the equation . Determine the speed of the point 2 s after the start of the motion.