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

1. Find the first derivative of y′

2. Find the first derivative of y′
2.20 s = et/cost

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.
3.20 x = et cost, y = et sint, t = π/4

4. Find the second derivative of y′′
4.20 y = xe−x3

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

6. Solve the following problems.
6.20. Find the equations of the tangent and normal to the curve 4х3 – 3ху2 + 6х2 – 5ху – 3y2 + 9х + 14 = 0 at the point (–2, 3).

7. Solve the following problems.
7.20. A point moves according to the law s = 4t3 + 2t2 – 5 (cm). Find the speed and acceleration of the point after 2 s.

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