IDZ Ryabushko Option 15 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′
2.15 y = etgxcosx

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.
3.15 y = (x + y)3 – 27(x – y), x = 2, y = 1

4. Find the second derivative of y′′
4.15 y = x3e5x

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

6. Solve the following problems.
6.15. Find the points at which the tangents to the graphs of the functions f(х) = х3 – х – 1 and φ(х) = 3х2 – 4х + 1 are parallel.

7. Solve the following problems.
7.15. A point moves along the hyperbola y = 10/x so that its abscissa increases uniformly at a speed of 1 m/s. At what speed does its ordinate change when the point passes position (5, 2)?