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)?

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