Ищем производные:
а) y=3x⁵ - 1 - ⁵√x = 3x⁵ - x⁻⁵ - x⁻¹/⁵
x⁵
y' = 15x⁴ + 5x⁻⁶ - 1 x⁻⁴/⁵ = 15x⁴ + 5 - 1
5 x⁶ 5 ⁵√x⁴
б) y=2√(4x+3) - 3
√(x³+x+1)
y' = 2*4 - 3(3x²+1) = 4 - 9x²+3
2√(4x+3) 2√(x³+x+1) √(4x+3) 2√(x³+x+1)
в) y=(lnx +1)² cos2x
y' = ((lnx+1)²)' cos2x + (lnx+1)² (cos2x)' =
=2(lnx+1) cos2x - 2sin2x (lnx+1)²
x