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)?

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