Решебник по алгебре и начала математического анализа 11 класс Колягин Задание 186

\[1)\ y = - \frac{2}{x^{4}} = - 2x^{- 4};\]

\[y^{'}(x) = - 2 \bullet \left( - 4x^{- 5} \right) = \frac{8}{x^{5}}.\]

\[2)\ y = 4x^{- \frac{3}{2}};\]

\[y^{'}(x) = 4 \bullet \left( - \frac{3}{2}x^{- \frac{5}{2}} \right) = - 6x^{- \frac{5}{2}}.\]

\[3)\ y = x^{- \frac{3}{2}} + 6x^{\frac{5}{6}};\]

\[y^{'}(x) = - \frac{3}{2}x^{- \frac{5}{2}} + 6 \bullet \frac{5}{6}x^{- \frac{1}{6}} =\]

\[= - 1,5x^{- \frac{5}{2}} + 5x^{- \frac{1}{6}}.\]

\[4)\ y = 2\sqrt[7]{x^{2}} - 3\sqrt[5]{x^{- 2}} =\]

\[= 2x^{\frac{2}{7}} - 3x^{- \frac{2}{5}};\]

\[y^{'}(x) = 2 \bullet \frac{2}{7}x^{- \frac{5}{7}} - 3 \bullet \left( - \frac{2}{5}x^{- \frac{7}{5}} \right) =\]

\[= \frac{4}{7}x^{- \frac{5}{7}} + \frac{6}{5}x^{- \frac{7}{5}}.\]

\[5)\ y = 6\sqrt[6]{x^{5}} - \frac{5}{\sqrt[5]{x^{4}}} =\]

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

\[y^{'}(x) = 6 \bullet \frac{5}{6}x^{- \frac{1}{6}} - 5 \bullet \left( \frac{4}{5}x^{- \frac{9}{5}} \right) =\]

\[= 5x^{- \frac{1}{6}} - 4x^{- \frac{9}{5}}.\]

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

\[= 2x^{\frac{5}{3}} + 4x^{- \frac{7}{4}};\]

\[y^{'}(x) = 2 \bullet \frac{5}{3}x^{\frac{2}{3}} + 4 \bullet \left( - \frac{7}{4}x^{- \frac{11}{4}} \right) =\]

\[= \frac{10}{3}x^{\frac{2}{3}} - 7x^{- \frac{11}{4}}.\]