Решебник по алгебре 11 класс Никольский Параграф 4. Производная Задание 39

\[\boxed{\mathbf{39}\mathbf{.}}\]

\[\textbf{а)}\ y = 7x^{4} - 5x^{3} - x + 25;\ \]

\[\ x \in R\]

\[y^{'} = 7 \cdot 4x^{3} - 5 \cdot 3x^{2} - 1 + 0 =\]

\[= 28x^{3} - 15x^{2} - 1.\]

\[\textbf{б)}\ y = - x^{4} + 8x^{2} + 2x - 19;\ \]

\[\ x \in R\]

\[y^{'} = - 4x^{3} + 8 \cdot 2x + 2 \cdot 1 - 0 =\]

\[= - 4x^{3} + 16x + 2.\]

\[\textbf{в)}\ y = x^{12} - 5x^{8} + 6x^{4} - 1;\ \ \]

\[x \in R\]

\[y^{'} = 12x^{11} - 5 \cdot 8x^{7} + 6 \cdot 4x^{3} -\]

\[- 0 = 12x^{11} - 40x^{7} + 24x^{3}.\]

\[\textbf{г)}\ y = 12x^{5} - 20x^{3} - 30x^{2};\ \ \]

\[x \in R\]

\[y^{'} = 12 \cdot 5x^{4} - 20 \cdot 3x^{2} -\]

\[- 30 \cdot 2x = 60x^{4} - 60x^{2} - 60x.\ \]