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.

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