Решебник по алгебре и начала математического анализа 11 класс Колягин Задание 198

\[1)\ y = 6x^{4} - 9e^{3x};\]

\[y^{'}(x) = 6 \bullet 4x^{3} - 9 \bullet 3e^{3x};\]

\[y^{'}(x) = 24x^{3} - 27e^{3x}.\]

\[2)\ y = \frac{1}{4}x^{8} + 3\sin{3x};\]

\[y^{'}(x) = \frac{1}{4} \bullet 8x^{7} + 3 \bullet 3\cos{3x};\]

\[y^{'}(x) = 2x^{7} + 9\cos{3x}.\]

\[3)\ y = 3\sqrt[3]{x} - 4\cos{4x};\]

\[y^{'}(x) = 3 \bullet \frac{1}{3}x^{- \frac{2}{3}} - 4 \bullet \left( - 4\sin{4x} \right);\]

\[y^{'}(x) = \frac{1}{\sqrt[3]{x^{2}}} + 16\sin{4x}.\]

\[4)\ y = \frac{5}{x^{2}} + 4e^{\frac{x}{4}};\]

\[y^{'}(x) = 5 \bullet \left( - \frac{2}{x^{3}} \right) + 4 \bullet \frac{1}{4}e^{\frac{x}{4}};\]

\[y^{'}(x) = - \frac{10}{x^{3}} + e^{\frac{x}{4}}.\]

\[5)\ y = \frac{1}{3x^{3}} + \frac{1}{2}\ln{4x};\]

\[y^{'}(x) = \frac{1}{3} \bullet \left( - \frac{3}{x^{4}} \right) + \frac{1}{2} \bullet 4 \bullet \frac{1}{4x};\]

\[y^{'}(x) = - \frac{1}{x^{4}} + \frac{1}{2x}.\]

\[6)\ y = 3\ tg\ 2x - 2\sqrt[3]{x};\]

\[y^{'}(x) = 3 \bullet 2 \bullet \frac{1}{\cos^{2}{2x}} - 2 \bullet \frac{1}{3}x^{- \frac{2}{3}};\]

\[y^{'}(x) = \frac{6}{\cos^{2}{2x}} - \frac{2}{3\sqrt[3]{x^{2}}}.\]