Решебник по алгебре и начала математического анализа 10 класс Алимов Задание 802

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

\[f^{'}(x) = \left( x^{2} \right)^{'} + (x)^{'} = 2x + 1\]

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

\[f^{'}(x) = \left( x^{2} \right)^{'} - (x)^{'} = 2x - 1\]

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

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

\[4)\ f(x) = - 17x^{2}\]

\[f^{'}(x) = - 17 \bullet \left( x^{2} \right)^{'} =\]

\[= - 17 \bullet 2x = - 34x\]

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

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

\[= - 4 \bullet 3x^{2} = - 12x^{2}\]

\[6)\ f(x) = 0,5x^{3}\]

\[f^{'}(x) = 0,5 \bullet \left( x^{3} \right)^{'} =\]

\[= 0,5 \bullet 3x^{2} = 1,5x^{2}\]

\[7)\ f(x) = 13x^{2} + 26\]

\[f^{'}(x) = 13 \bullet \left( x^{2} \right)^{'} + (26)^{'} =\]

\[= 13 \bullet 2x + 0 = 26x\]

\[8)\ f(x) = 8x^{2} - 16\]

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

\[= 8 \bullet 2x - 0 = 16x.\]