Решебник по алгебре 11 класс Никольский Параграф 4. Производная Задание 60

\[\boxed{\mathbf{60}\mathbf{.}}\]

\[\textbf{а)}\ f(x) = (2x + 1)^{8};\ \ x \in R\]

\[f^{'}(x) = 2 \cdot 8 \cdot (2x + 1)^{7} =\]

\[= 16(2x + 1)^{7}.\]

\[\textbf{б)}\ f(x) = ( - 2x - 3)^{9};\ \ x \in R\]

\[f^{'}(x) = - 2 \cdot 9 \cdot ( - 2x - 3)^{8} =\]

\[= - 18( - 2x - 3)^{9}.\]

\[\textbf{в)}\ f(x) = (4x - 3)^{10};\ \ x \in R\]

\[f^{'}(x) = 4 \cdot 10 \cdot (4x - 3)^{9} =\]

\[= 40(4x - 3)^{9}.\]

\[\textbf{г)}\ f(x) = (3x + 4)^{25};\ \ x \in R\]

\[f^{'}(x) = 3 \cdot 25 \cdot (3x + 4)^{24} =\]

\[= 75(3x + 4)^{24}.\]