Решебник по алгебре и начала математического анализа 11 класс Колягин Задание 172

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

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

\[= 6(2x - 1)^{2}.\]

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

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

\[= 2x + 6.\]

\[3)\ f(x) = \left( 3x^{2} - 2x \right)^{2};\]

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

\[= (12x - 4)\left( 3x^{2} - 2x \right).\]

\[4)\ f(x) = \left( x^{3} - x^{2} \right)^{3};\]

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

\[= \left( 9x^{2} - 6x \right)\left( x^{3} - x^{2} \right)^{2}.\]