6) y = \frac{x}{3}-\frac{4}{x^2}+√x;

Найдем производную функции y = x/3 - 4/x² + √x.

Перепишем функцию: y = (1/3) * x - 4 * x^(-2) + x^(1/2)

y' = (1/3 * x)' - (4 * x^(-2))' + (x^(1/2))'

(1/3 * x)' = 1/3

(4 * x^(-2))' = 4 * (-2) * x^(-3) = -8x^(-3) = -8 / x³

(x^(1/2))' = 1/2 * x^(-1/2) = 1 / (2√x)

Тогда:

y' = 1/3 - (-8 / x³) + 1 / (2√x) = 1/3 + 8 / x³ + 1 / (2√x)

Ответ: y' = 1/3 + 8 / x³ + 1 / (2√x)