IDZ Ryabushko Option 12 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′
2.12 y = cos2x∙sin2x

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.
3.12 f(x) = ln(1 + x) + arcsin(x/2), x = 1

4. Find the second derivative of y′′
4.12 y = x/√1 − x2

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

6. Solve the following problems.
6.12. Write equations of the tangent and normal to the semi-cubic parabola x = t2, y = t3 drawn at the point t = 2.

7. Solve the following problems.
7.12. The wheel rotates so that the angle of rotation is proportional to the cube of time. The first two revolutions were made by the wheel in 4 s. Find the angular velocity ω of the wheel 16 s after the start of the movement.