IDZ Ryabushko Option 17 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′
2.17 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?