Решебник по алгебре и начала математического анализа 11 класс Колягин Задание 352

\[1)\ F(x) = x^{4};\text{\ \ \ f}(x) = 4x^{3}:\]

\[F^{'}(x) = 4x^{3} = f(x).\]

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

\[F^{'}(x) = 0 - \left( - e^{- x} \right) = e^{- x} = f(x).\]

\[3)\ F(x) = \frac{x^{5}}{5} + 1;\text{\ \ \ f}(x) = x^{4}:\]

\[F^{'}(x) = \frac{1}{5} \bullet 5x^{4} + 0 = x^{4} = f(x).\]

\[4)\ F(x) = 3e^{\frac{x}{3}};\text{\ \ \ f}(x) = e^{\frac{x}{3}}:\]

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

\[5)\ F(x) = 2 + \sin{4x};\text{\ \ \ }\]

\[f(x) = 4\cos{4x}:\]

\[F^{'}(x) = 0 + 4\cos{4x} =\]

\[= 4\cos{4x} = f(x).\]

\[6)\ F(x) = \cos{3x} - 5;\text{\ \ \ }\]

\[f(x) = - 3\sin{3x}:\]

\[F^{'}(x) = - 3\sin{3x} - 0 =\]

\[= - 3\sin{3x} = f(x).\]