IDZ Ryabushko Option 13 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′
2.13 y = sin35x∙sin53x

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.
3.13 f(x) = tg3(πx/6), x = 2

4. Find the second derivative of y′′
4.13 y = (lnx)/x

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

6. Solve the following problems.
6.13. Find the angle of intersection of the curves x2 + y2 = 5 and y2 = 4x.

7. Solve the following problems.
7.13. The body moves along a straight line Ox according to the law x = t3/3 – 2t2 + 3t. Determine the speed and acceleration of the motion. At what moments does the body change the direction of motion?