ГДЗ по алгебре и начала математического анализа 10 класс Алимов Задание 830

\[\boxed{\mathbf{830}\mathbf{.}}\]

\[f(x) = \sqrt{x^{2} - 5x + 6}\]

\[u = x^{2} - 5x + 6\ f(u) = \sqrt{u}:\]

\[f^{'}(x) = \left( x^{2} - 5x + 6 \right)^{'} \bullet \left( \sqrt{u} \right)^{'} =\]

\[= (2x - 5) \bullet \frac{1}{2\sqrt{u}} =\]

\[= \frac{2x - 5}{2\sqrt{x^{2} - 5x + 6}}.\]

\[x^{2} - 5x + 6 > 0\]

\[D = 25 - 24 = 1\]

\[x_{1} = \frac{5 - 1}{2} = 2\]

\[x_{2} = \frac{5 + 1}{2} = 3\]

\[(x - 2)(x - 3) > 0\]

\[x < 2\ или\ x > 3.\]

\[Ответ:\ \ \frac{2x - 5}{2\sqrt{(x - 2)(x - 3)}}.\]