IDZ Ryabushko Option 16 KR "Derivatives and their appl

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

1. Find the first derivative of y′

2. Find the first derivative of y′
2.16 y = arcsin(tgx)

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.
3.16 yey = ex + 1, x = 0, y = 1

4. Find the second derivative of y′′
4.16 y = (1 + x2)tgx

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

6. Solve the following problems.
6.16. Write the equations of the tangents and normals to the curve x2 + y2 + 4x – 2y – 3= 0 at the points of its intersection with the Oy axis.

7. Solve the following problems.
7.16. The law of motion of a point along the Ox axis s = 5t – t2. Find the speed and acceleration of the point for the moments of time t1 = 0, t2 = 1 s