Решебник по алгебре и начала математического анализа 11 класс Колягин Задание 207

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

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

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

\[2)\ y = \ln\left( 3 - 4x^{2} \right);\]

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

\[= \frac{8x}{4x^{2} - 3}.\]

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

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

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

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

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

\[= - \frac{2e^{\frac{1}{2x + 3}}}{(2x + 3)^{2}}.\]

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

\[= \frac{8x}{3 - 4x^{2}}.\]

\[6)\ y = \ln\frac{3}{2x^{2} + 7x};\]

\[= - \frac{4x + 7}{2x^{2} + 7x}.\]