IDZ Ryabushko Option 23 KR "Derivatives and their appli
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Test "Derivatives and their applications" (2 hours). 260 pages
1. Find the first derivative of y′
2. Find the first derivative of y′
2.23 y = √1 + ln2x
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.
3.23 φ(z) = z(1 + √z3) , z = 0
4. Find the second derivative of y′′
4.23 y = xesinx
5. Find the second derivative d2y/dx2 of the function.
6. Solve the following problems.
6.23. Find the distance from the vertex of the parabola y = x2 – 4x + 5 to the tangent to it at the point of intersection of the parabola with the Oy axis.
7. Solve the following problems.
7.23. At what point of the ellipse 16x2 + 9y2 = 400 does the ordinate decrease at the same rate as the abscissa increases?
1. Find the first derivative of y′
2. Find the first derivative of y′
2.23 y = √1 + ln2x
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.
3.23 φ(z) = z(1 + √z3) , z = 0
4. Find the second derivative of y′′
4.23 y = xesinx
5. Find the second derivative d2y/dx2 of the function.
6. Solve the following problems.
6.23. Find the distance from the vertex of the parabola y = x2 – 4x + 5 to the tangent to it at the point of intersection of the parabola with the Oy axis.
7. Solve the following problems.
7.23. At what point of the ellipse 16x2 + 9y2 = 400 does the ordinate decrease at the same rate as the abscissa increases?
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