IDZ Ryabushko Option 28 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′
2.28 y = ln(ex + √1 + e2x)

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.
3.28 y = 3√tg(x/2), x = π/2

4. Find the second derivative of y′′
4.28 y = sinx − 1/3cos3x

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

6. Solve the following problems.
6.28. Write the equation of the tangent to the line y = arctg(x/2) at the points of its intersection with the line x – 2 = 0.

7. Solve the following problems.
7.28. A point moves in a straight line such that υ2 = 2bx, where υ is the speed of the point; x is the distance traveled; b is some constant. Determine the acceleration of the point.