IDZ Ryabushko Option 22 KR "Derivatives and their appli

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.