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

1. Find the first derivative of y′

2. Find the first derivative of y′
2.30 y = tg2(x3 + 1)

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.
3.30 F(x) = 1/(x + 2) + 3/(x2 + 1), x = 0, x = 1

4. Find the second derivative of y′′
4.30 y = ln(x + √x)

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

6. Solve the following problems.
6.30. At what value of the parameter a does the parabola y = ax3 touch the curve y = ln x?

7. Solve the following problems.
7.30. A point moves in a straight line according to the law s = 60t – 5t3. After what period of time after the start of the motion will the point stop? Find the path traveled by the point during this time.

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