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?

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