5. Найдите производную функции: a) y = 4cos x - 7/x⁴; b) y = 3x * sin x; v) y = (4x² - x) / (3x); r) y = (7x + 4)⁵; d) y = √(9 - 6x).

a) y = 4cos x - 7/x⁴ = 4cos x - 7x⁻⁴ y' = -4sin x - 7 * (-4)x⁻⁵ = -4sin x + 28x⁻⁵ = -4sin x + 28/x⁵ **Ответ: y' = -4sin x + 28/x⁵** b) y = 3x * sin x y' = (3x)' * sin x + 3x * (sin x)' = 3sin x + 3xcos x **Ответ: y' = 3sin x + 3xcos x** v) y = (4x² - x) / (3x) = (4x²)/(3x) - x/(3x) = (4/3)x - 1/3 y' = 4/3 **Ответ: y' = 4/3** r) y = (7x + 4)⁵ y' = 5(7x + 4)⁴ * (7x + 4)' = 5(7x + 4)⁴ * 7 = 35(7x + 4)⁴ **Ответ: y' = 35(7x + 4)⁴** d) y = √(9 - 6x) = (9 - 6x)^(1/2) y' = (1/2)(9 - 6x)^(-1/2) * (9 - 6x)' = (1/2)(9 - 6x)^(-1/2) * (-6) = -3 / √(9 - 6x) **Ответ: y' = -3 / √(9 - 6x)**