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

1. Find the first derivative of y′

2. Find the first derivative of y′
2.21 y = (1 + ex)/(1 – ex)

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.
3.21 y(x) = (1 + x3)(5 – 1/ x2), x = 1, x = 0

4. Find the second derivative of y′′
4.21 y = arctan(2x/(1 – x2))

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

6. Solve the following problems.
6.21. Write the equation of the normal to the astroid x = acos3t, y = asin3t at the point for which t = π/4.

7. Solve the following problems.
7.21. The radius of a sphere increases uniformly at a rate of 5 cm/s. At what rate do the surface area of ​​the sphere and its volume increase at the moment when its radius becomes equal to 50 cm?

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