1) y = 5(3x² -5x +9)¹⁰
y' = 50(3x² -5x +9)⁹ * (3x² -5x +9)' = 50(3x² -5x +9)⁹ *(6x -5)
2)y = 2√(1 + 2x³ - x⁵)
y' = 1/(2√(1 + 2x³ - x⁵) ) * (1 + 2x³ - x⁵)' = (6x² -5x⁴)/ (2√(1 + 2x³ - x⁵) )
3) у = √(6 -7х +2х²)
y' =1 /(2√(6 - 7x +2x²) ) * (6 -7x +2x²)' = (-7x +4x)/(2√(6 - 7x +2x²) )
4) у = √(х³ -1)
y' = 1/(2√(x³-1)) * (x³ -1)' = 3x²/(2√(x³-1))
5) y = √2/(2x² +1)
y' = 1/(2√2/(2x² +1)) * (2/(2x² +1) )' = - 1/(2√2/(2x² +1)) * 8x/2x² +1)²