Решебник по алгебре 11 класс Никольский Параграф 4. Производная Задание 17

\[\boxed{\mathbf{17}\mathbf{.}}\]

\[\textbf{а)}\ y = x^{2} + x\]

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

\[\textbf{б)}\ y = x^{2} - x\]

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

\[\textbf{в)}\ y = x^{2} + 14\]

\[y^{'} = \left( x^{2} \right)^{'} + 14^{'} = 2x + 0 = 2x.\]

\[\textbf{г)}\ y = x^{2} - 15\]

\[y^{'} = \left( x^{2} \right)^{'} - 15^{'} = 2x - 0 = 2x.\]

\[\textbf{д)}\ y = 5x^{2}\]

\[y^{'} = \left( {5x}^{2} \right)^{'} = 5 \cdot \left( x^{2} \right)^{'} =\]

\[= 5 \cdot 2x = 10x.\]

\[\textbf{е)}\ y = - x^{2}\]

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

\[\textbf{ж)}\ y = 5x^{2} + 3x\]

\[y^{'} = 5 \cdot \left( x^{2} \right)^{'} + 3 \cdot x^{'} = 5 \cdot 2x +\]

\[+ 3 \cdot 1 = 10x + 3.\]

\[\textbf{з)}\ y = 3x^{2} - 3x + 1\]

\[y^{'} = 3 \cdot \left( x^{2} \right)^{'} - 3 \cdot x^{'} + 1^{'} =\]

\[= 3 \cdot 2x - 3 \cdot 1 + 0 = 6x - 3.\]

\[\textbf{и)}\ y = ax^{2} + bx + c;\ \ x \in R\]

\[y^{'} = a \cdot \left( x^{2} \right)^{'} + b \cdot x^{'} + c^{'} =\]

\[= a \cdot 2x + b \cdot 1 + 0 = 2ax + b.\]