Решебник по алгебре и начала математического анализа 11 класс Колягин Задание 164

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

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

\[2)\ f(x) = 6x^{2} + 5x - 7;\]

\[f^{'}(x) = 6 \bullet 2x + 5 = 12x + 5.\]

\[3)\ f(x) = x + 12x^{2};\]

\[f^{'}(x) = 1 + 12 \bullet 2x = 1 + 24x.\]

\[4)\ f(x) = x - 8x^{2};\]

\[f^{'}(x) = 1 - 8 \bullet 2x = 1 - 16x.\]

\[5)\ f(x) = x^{3} + 6x;\]

\[f^{'}(x) = 3x^{2} + 6.\]

\[6)\ f(x) = - 12x^{3} + 18x;\]

\[f^{'}(x) = - 12 \bullet 3x^{2} + 18 =\]

\[= - 36x^{2} + 18.\]

\[7)\ f(x) = 2x^{3} - 8x^{2} + 6x + 1;\]

\[f^{'}(x) = 2 \bullet 3x^{2} - 8 \bullet 2x + 6 =\]

\[= 6x^{2} - 16x + 6.\]

\[8)\ f(x) = - 3x^{3} + 2x^{2} - x - 5;\]

\[f^{'}(x) = - 3 \bullet 3x^{2} + 2 \bullet 2x - 1 =\]

\[= - 9x^{2} + 4x - 1.\]