IDZ Ryabushko Option 9 KR "Derivatives and their applic

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

1. Find the first derivative of y′

2. Find the first derivative of y′
2.9 y = 3xcos3x

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.
3.9 f(x) = x2 – 1/(2x2), x = ± 2

4. Find the second derivative of y′′
4.9 y = xe–x

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

6. Solve the following problems.
6.9. Find the angle of intersection of the lines y = 1 + sinх and y = 1.

7. Solve the following problems.
7.9. A body with a mass of 6 tons moves in a straight line according to the law s = −1 + ln(t + 1) + (t + 1)3. It is required to calculate the kinetic energy mυ2/2 of the body 1 s after the start of the motion.