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

1. Find the first derivative of y′

2. Find the first derivative of y′
2.7 y = e−1/cosx

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.
3.7 f(x) = 3√x2, x = –8

4. Find the second derivative of y′′
4.7 y = 2cotg3x

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

6. Solve the following problems.
6.7. At what value of a does the curve y = (ax + x3)/4 intersect the Ox axis at an angle of 45°?

7. Solve the following problems.
7.7. The raft is pulled to the shore by a rope that is wound onto a winch at a speed of 50 m/min. Determine the speed of the raft at the moment when its distance from the shore is 25 m, if the winch is located on the shore 6√6 m above the water surface.

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