IDZ Ryabushko Option 14 KR "Derivatives and their appli

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

1. Find the first derivative of y′

2. Find the first derivative of y′
2.14 Q = ecos23φ

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.
3.14 2y = 1 + xy3, x = 1, y = 1

4. Find the second derivative of y′′
4.14 y = x2lnx3

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

6. Solve the following problems.
6.14. Determine the angle at which the curve y = (x – 1)/(1 + x2) intersects the abscissa axis.

7. Solve the following problems.
7.14. A point moves along the parabola y = x(8 – x) so that its abscissa changes depending on time t according to the law x = t√t. What is the rate of change of the ordinate at the point M(1, 7)?