Ryabushko A.P. IDZ 6.2 option 10

DHS - 6.2
Find y ´and y ".
№ 1.10. xy = ctg x.
№ 2.10. {X = L (t) / t; y = t Ln t.
№ 3.10. For a given function y and calculate the argument x0 ‴ y (x0); y = x²eˣ; x0 = 0.
№ 4.10. Write a formula for the derivative of n - th order for the function y = x e³ˣ;
№ 5.10. Write the equation of the tangent to the curve y = x² / 4 - 4x + 5; at the point with the abscissa x = 4.
№ 6.10. The law of motion of a material point S = -3 cos (t / 4 + π / 12). Find its velocity at time t = 2π / 3c.