IDZ Ryabushko Option 19 KR "Derivatives and their appli

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

1. Find the first derivative of y′

2. Find the first derivative of y′
2.19 z = (siny)/(1 + tgy)

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.
3.19 x = a(t – sint), y = a(1 – cost), t = π/2

4. Find the second derivative of y′′
4.19 y = √xex

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

6. Solve the following problems.
6.19. On the parabola y = x2 + 5x + 3, two points with abscissas x = −2 and x = 3 are taken. At what point of the parabola will the tangent to it be parallel to the secant drawn through these points?

7. Solve the following problems.
7.19 A point moves along the curve y = 3√x in the first quadrant. Find the coordinates of the point at the moment when the rate of change of the abscissa of this point is 12 times greater than the rate of change of its ordinate.