Решебник по алгебре 11 класс Никольский Параграф 4. Производная Задание 59

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\[\textbf{а)}\ f(x) = \ln{3x};\ \ x > 0\]

\[f^{'}(x) = \frac{1}{3x} \cdot 3 = \frac{1}{x}.\]

\[\textbf{б)}\ f(x) = \ln(5 - 2x);\]

\[\ \ 5 - 2x > 0;\ \ x < 2,5\]

\[f^{'}(x) = \frac{1}{5 - 2x} \cdot ( - 2) = \frac{2}{2x - 5}.\]

\[\textbf{в)}\ f(x) = \log_{5}( - 3x - 1);\ \]

\[- 3x - 1 > 0;\ \ x < - \frac{1}{3}\]

\[f^{'}(x) = \frac{1}{( - 3x - 1)\ln 5} \cdot ( - 3) =\]

\[= \frac{3}{(3x + 1)\ln 5}.\]

\[\textbf{г)}\ f(x) = \lg(2x + 4);\ \ \ \]

\[2x + 4 > 0;\ \ x > - 2\]

\[f^{'}(x) = \frac{1}{(2x + 4)\ln 10} \cdot 2 =\]

\[= \frac{1}{(x + 2)\ln 10}.\]