Решебник по алгебре и начала математического анализа 11 класс Алимов Задание 1545

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\[1)\ f(x) = (2x - 1)^{3}\]

\[u = 2x - 1;f(u) = u^{3}:\]

\[f^{'}(x) = (2x - 1)^{'} \bullet \left( u^{3} \right)^{'} =\]

\[= 2 \bullet 3u^{2} = 6(2x - 1)^{2};\]

\[(2x - 1)^{2} = 0\]

\[2x - 1 = 0\]

\[2x = 1\]

\[x = \frac{1}{2}.\]

\[Ответ:\ \ x = \frac{1}{2}.\]

\[2)\ f(x) = (1 - 3x)^{5}\]

\[u = 1 - 3x;\ \ \ f(u) = u^{5}:\]

\[f^{'}(x) = (1 - 3x)^{'} \bullet \left( u^{5} \right)^{'} =\]

\[= - 3 \bullet 5u^{4} = - 15(1 - 3x)^{4};\]

\[(1 - 3x)^{4} = 0\]

\[1 - 3x = 0\]

\[3x = 1\]

\[x = \frac{1}{3}.\]

\[Ответ:\ \ x = \frac{1}{3}.\]