13)y= --2√x/x⁶-2

Найдем производную функции: $$y = \frac{-2\sqrt{x}}{x^6 - 2}$$

Применим правило производной частного: $$(\frac{u}{v})' = \frac{u'v - uv'}{v^2}$$

Пусть $$u = -2\sqrt{x}$$ и $$v = x^6 - 2$$. Тогда $$u' = -\frac{1}{\sqrt{x}}$$ и $$v' = 6x^5$$

$$y' = \frac{(-\frac{1}{\sqrt{x}})(x^6 - 2) - (-2\sqrt{x})(6x^5)}{(x^6 - 2)^2} = \frac{-\frac{x^6}{\sqrt{x}} + \frac{2}{\sqrt{x}} + 12x^5\sqrt{x}}{(x^6 - 2)^2} = \frac{-x^{5.5} + 2x^{-0.5} + 12x^{5.5}}{(x^6 - 2)^2} = \frac{11x^{5.5} + 2x^{-0.5}}{(x^6 - 2)^2} = \frac{11x^6 + 2}{x^{0.5}(x^6 - 2)^2}$$

Ответ: $$y' = \frac{11x^6 + 2}{\sqrt{x}(x^6 - 2)^2}$$