А) y=9x³ -7∛x⁸ + 3 - 2⁴√5 = 9x³ - 7x^(⁸/₃) +3x⁻⁸ - 2⁴√5
x⁸
y' = 9*3x² - 7* (⁸/₃) x^(⁸/₃ - ³/₃) + 3 * (-8)x⁻⁸⁻¹ - 0 =
= 27x² - ⁵⁶/₃ x^(⁵/₃) - 24x⁻⁹ =
= 27x² - 18 ²/₃ ∛x⁵ - 24
x⁹
б) y=√x cosx
y' = (√x)' cosx + √x (cosx)' = cosx - √x sinx
2√x
в) y= arctgx
e^x - sinx
y' = (arctgx)' (e^x - sinx) - arctgx (e^x - sinx)' =
(e^x - sinx)²
= e^x - sinx - arctgx (e^x - cosx) = e^x-sinx-(1+x²) arctgx (e^x - cosx)
1+x² (1+x²)(e^x-sinx)²
(e^x-sinx)²
г) y=log₇ sinx
y' = cosx = ctgx
(sinx)ln7 ln7
д) y= √(1-sinx) +2= -cosx
2√(1-sinx)