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

1. Find the first derivative of y′

2. Find the first derivative of y′

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.
3.25 φ(z) = (a – z)/(1 + z), z = 1

4. Find the second derivative of y′′
4.25 y = xarctgx

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

6. Solve the following problems.
6.25. Draw a tangent to the curve y = (x + 9)/(x + 5) so that it passes through the origin. Write the equation of this tangent.

7. Solve the following problems.
7.25. The wheel rotates so that the angle of rotation is proportional to the square of time. The first revolution was made by the wheel in 8 s. Find the angular velocity ω of the wheel 32 s after the start of the movement.

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