Option 3 DHS 6.2

Option 3 DHS 6.2

DHS - 6.2
Find y´ and y. "
No. 1.3. y = x + arctg y.
Find y´ and y. "
No. 2.3. {x = 6cos³t; y = 2sin³t
No. 3.3. For a given function y and argument x0, calculate y´´´ (x0); y = ln (2 + x²) arctg x; xo = 0.
No. 4.3. Write the formula for the derivative of the nth order for the function y = 2ˣ;
No. 5.3. Write the equation of the tangent to the curve y = √x - 4; at the point with the x = 8 abscissa.
No. 6.3. Two material points move along the Ox axis; the laws of motion are x = 4t² - 7 and y = 3t²- 4t + 38. At what speed do these points move away from each other at the time of the meeting?