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

1. Find the first derivative of y′

2. Find the first derivative of y′
2.5 y = e−φ2cos3(2φ + 3)

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.
3.5 f(t) = √a2 + b2 − 2abcost , t = π/2

4. Find the second derivative of y′′
4.5 y = lnctg4x

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

6. Solve the following problems.
6.5. On the parabola y = x2, two points with abscissas x1 = 1 and x2 = 3 are taken. A secant is drawn through these points. At what point of the parabola is the tangent to it parallel to the secant?

7. Solve the following problems.
7.5. A body with a mass of 100 kg moves in a straight line according to the law s = 2t2 + 3t + 1. Determine the kinetic energy mυ2/2 of the body 5 s after the start of the motion.

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