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)
![y' = ( \frac{2}{3x-4})' = \frac{2' * (3x-4) - 2 * (3x-4)'}{(3x-4) ^{2} } = - \frac{6}{(3x-4) ^{2} }](https://tex.z-dn.net/?f=y%27+%3D+%28+%5Cfrac%7B2%7D%7B3x-4%7D%29%27+%3D++%5Cfrac%7B2%27+%2A+%283x-4%29+-+2+%2A+%283x-4%29%27%7D%7B%283x-4%29+%5E%7B2%7D+%7D+%3D+-++%5Cfrac%7B6%7D%7B%283x-4%29+%5E%7B2%7D+%7D+)
![y'' = [ -6(3x-4) ^{-2}]' = 12(3x-4) ^{-3} * (3x-4)' = 36(3x-4) ^{-3} =](https://tex.z-dn.net/?f=y%27%27+%3D+%5B+-6%283x-4%29+%5E%7B-2%7D%5D%27+%3D+12%283x-4%29+%5E%7B-3%7D+%2A+%283x-4%29%27+%3D+36%283x-4%29+%5E%7B-3%7D+%3D+)
![\frac{36}{(3x-4) ^{3} }](https://tex.z-dn.net/?f=+%5Cfrac%7B36%7D%7B%283x-4%29+%5E%7B3%7D+%7D+)
(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