IDZ Ryabushko Option 20 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′
2.20 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.