Option 30 DHS 6.2

Option 30 DHS 6.2

DHS - 6.2
Find y´ and y. "
No. 1.30. ctg² (x + y) = 5x.
Find y´ and y. "
No. 2.30. {x = arcsin t; y = ln t.
No. 3.30. For a given function y and argument x0, calculate y ‴ (x0); y = sin (x³ + π); x0 = ³√π.
No. 4.30. Write the formula for the derivative of the nth order for the function y = ln (5x-1);
No. 5.30. Find out at what point of the curve y = x² / 4 - 7x + 5; the tangent is parallel to the line y = 2x + 5.
No. 6.30. The law of motion of the material point S = 3t + t³. Find the speed of its movement at time t = 2 s.