Решение
1) y = 3 / (x + 2)⁵ - (5x - 7x² - 3)¹/⁷
y` = [3 * (x + 2)⁻⁵]` - [(5x - 7x² - 3)¹/⁷]`
y` = 3*(-5)*(x + 2)⁻⁶ - (1/7) * (5x - 7x² - 3) ⁻⁶/⁷ * (5 - 14x) =
= - 15 / (x + 2)⁶ - (5 - 14x) / [7*(5x - 7x² - 3)⁶/⁷]
2) y = cos³4x * arcctg√x
y` = (cos³4x)` * arcctg√x + (arcctg√x)` * (cos³4x) =
= [3*cos²4x * (- sin4x) * 4] * arcctg√x + [ - 1 / ( 1 + x²)] * (1/2√x) * cos³4x =
= -12*cos²4x * sin4x * arcctg√x - cos³4x / [2√x ( 1 + x²)]