Решебник по алгебре и начала математического анализа 11 класс Колягин Задание 205

\[1)\ y = e^{\frac{1}{x}};\]

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

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

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

\[= \frac{2}{x^{2}} \bullet e^{- \frac{2}{x}}.\]

\[3)\ y = \ln(2x - 1);\]

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

\[4)\ y = \ln{3x};\]

\[y^{'}(x) = 3 \bullet \frac{1}{3x} = \frac{1}{x}.\]

\[5)\ y = tg\frac{x}{2};\]

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

\[6)\ y = \cos{4x};\]

\[y^{'}(x) = - 4\sin{4x}.\]

\[7)\ y = tg(3x + 3);\]

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

\[8)\ y = \sin\left( \frac{2x}{3} + 1 \right);\]

\[y^{'}(x) = \frac{2}{3}\cos\left( \frac{2x}{3} + 1 \right).\]