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

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