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.

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