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

1. Find the first derivative of y′

2. Find the first derivative of y′

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.
3.11 f(x) = e−xcos3x, x = 0

4. Find the second derivative of y′′
4.11 y = x√1 + x2

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

6. Solve the following problems.
6.11. Find the angle of intersection of the curves y = x3 and y = 1/x2.

7. Solve the following problems.
7.11. The relationship between the amount x of a substance obtained as a result of a certain reaction and time t is expressed by the equation x = 7(1 – e–3t). Determine the reaction rate 2 s after the start of the experiment (t = 0).

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