1) y = 5x²² + 3
y' = (5x²²)' + 3' = 66x²¹
y'' = (66x²¹)' = 1386x²⁰
y''' = (1386x²⁰)' = 27 720 x¹⁹
2) y = ctg(π/3 - x)
y' = [ctg(π/3 - x)]' = - 1/Sin²(π/3 - x)* (π/3 - x)' = 1/Sin²(π/3 - x)
y'' = [1/Sin²(π/3 - x)]' = [Sin⁻²(π/3 - x)]' = - 2Sin⁻³(π/3 - x) * (π/3 - x)' =
= 2Sin⁻³(π/3 - x) = 2 / Sin³(π/3 - x)
3)
(sinx/2)^2-(cosx/2)^2=(2^1/2)/2
-cosx=(2^1/2)/2
cosx=-(2^1/2)/2
x=+-arccos(-(2^1/2)/2)+2пк, к -целое число
x=+-3п/4+2пк