Решебник по алгебре и начала математического анализа 11 класс Колягин Задание 179

\[1)\ f(x) = x^{6};\]

\[f^{'}(x) = 6x^{5}.\]

\[2)\ f(x) = x^{12};\]

\[f^{'}(x) = 12x^{11}.\]

\[3)\ f(x) = 3x^{4} + 2x^{13};\]

\[f^{'}(x) = 3 \bullet 4x^{3} + 2 \bullet 13x^{12} =\]

\[= 12x^{3} + 26x^{12}.\]

\[4)\ f(x) = 7x^{3} - 3x^{7};\]

\[f^{'}(x) = 7 \bullet 3x^{2} - 3 \bullet 7x^{6} =\]

\[= 21x^{2} - 21x^{6}.\]

\[5)\ f(x) = \frac{3}{x^{4}} = 3x^{- 4};\]

\[f^{'}(x) = 3 \bullet \left( - 4x^{- 5} \right) = - \frac{12}{x^{5}}.\]

\[6)\ f(x) = x^{3} + \frac{1}{x^{2}} = x^{3} + x^{- 2};\]

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