Test "Derivatives and their applications" (2 hours). 260 pages

1. Find the first derivative of y′

2. Find the first derivative of y′
2.17 y = ecosx sin2x

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.
3.17 y2 = x + ln(y/x), x = 1, y = 1

4. Find the second derivative of y′′
4.17 y = excos4x

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

6. Solve the following problems.
6.17. Write the equations of the tangents and normals to the curve y = 4x – x3 at the points of its intersection with the Ox axis.

7. Solve the following problems.
7.17. A point moves along a parabola y = √6x so that its abscissa increases at a speed of 10 cm/s. What is the rate of change of the ordinate at this point at the moment when x = 6?

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