ГДЗ по алгебре и начала математического анализа 11 класс Колягин Задание 353

\[x > 0.\]

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

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

\[2)\ F(x) = \frac{1}{\sqrt{x}} + 4;f(x) = - \frac{1}{2x^{\frac{3}{2}}}:\]

\[F^{'}(x) = - \frac{1}{2}x^{- \frac{3}{2}} + 0 = - \frac{1}{2x^{\frac{3}{2}}} = f(x).\]

\[3)\ F(x) = 2 - x^{\frac{3}{2}};f(x) = - \frac{3}{2}\sqrt{x}:\]

\[F^{'}(x) = 0 - \frac{3}{2}x^{\frac{1}{2}} = - \frac{3}{2}\sqrt{x} = f(x).\]

\[4)\ F(x) = \sqrt{2x};\text{\ f}(x) = \frac{1}{\sqrt{2x}}:\]

\[F^{'}(x) = \frac{1}{2\sqrt{2x}} \bullet 2 = \frac{1}{\sqrt{2x}} = f(x).\]