ГДЗ по алгебре и начала математического анализа 10 класс Алимов Задание 1550

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\[1)\ y = \frac{x^{5} - 3x^{3} + 2x^{2} - x + 3}{x^{3}} =\]

\[= x^{2} - 3 + 2x^{- 1} - x^{- 2} + 3x^{- 3};\]

\[= 2x - \frac{2}{x^{2}} + \frac{2}{x^{3}} - \frac{9}{x^{4}} =\]

\[= \frac{2x^{5} - 2x^{2} + 2x - 9}{x^{4}}.\]

\[2)\ y = \frac{6x\sqrt[3]{x}}{\sqrt{x}} = \frac{6x \bullet x^{\frac{1}{3}}}{x^{\frac{1}{2}}} = \frac{6x^{\frac{4}{3}}}{x^{\frac{1}{2}}} =\]

\[= 6x^{\frac{4}{3} - \frac{1}{2}} = 6x^{\frac{5}{6}};\]

\[y^{'}(x) = 6\left( x^{\frac{5}{6}} \right)^{'} = 6 \bullet \frac{5}{6}x^{- \frac{1}{6}} =\]

\[= 5x^{- \frac{1}{6}} = \frac{5}{\sqrt[6]{x}}.\]