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

1. Find the first derivative of y′

2. Find the first derivative of y′
2.22 y = sin23x

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.
3.22 s(t) = 3/(5 – t) + t2/5, t = 0, t = 2

4. Find the second derivative of y′′
4.22 y = x3lnx

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

6. Solve the following problems.
6.22. Write an equation of the normal to the curve y = ln(2x + 1) that is perpendicular to the bisector of the first and third coordinate angles.

7. Solve the following problems.
7.22. The electric charge passing through a conductor, starting from the moment of time t = 0, is given by the formula Q = 2t2 + 10t + 9. Find the current for t = 15 s.

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