IDZ Ryabushko Option 18 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′

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.
3.18 x = tlnt, y = (lnt)/t, t = 1

4. Find the second derivative of y′′
4.18 y = e−xcosx

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

6. Solve the following problems.
6.18. Write the equation of the tangents to the hyperbola хy = 4 at points with abscissas x1 = 1, x2 = −4 and find the angle between the tangents.

7. Solve the following problems.
7.18. The law of motion of a point along a straight line is given by the formula s = 5t – 4/t2 + 3. Find the speed and acceleration of the point 1 s after the start of the motion.