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

1. Find the first derivative of y′

2. Find the first derivative of y′
2.8 y = 3√(1 + sin32x)2

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.
3.8 f(x) = (√x− 1)2/x, x = 0.01

4. Find the second derivative of y′′
4.8 y = xe1/x

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

6. Solve the following problems.
6.8. Find the angle of intersection of the curve y = x – x3 and the line y = 5x.

7. Solve the following problems.
7.8. The charge passing through a conductor, starting from the moment of time t = 0, is determined by the formula Q = t3 – 9t2 + 15t + 1. At what moments in time will the current in the conductor be zero?

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