вправа 19.6 гдз 10 клас математика Мерзляк Номіровський 2018
Вправа 19.6
Умова:
Умова:
Продиференціюйте функцію.
Відповідь ГДЗ:
\begin{equation} 1){y}'= {\left ( \sqrt[4]{x} \right )}'=\frac{1}{4\sqrt[4]{x^{3}}}; \end{equation} \begin{equation} 2){y}'={\left ( \sqrt[8]{x^{7}} \right )}'= \end{equation} \begin{equation} ={\left ( x^{\frac{7}{8}} \right )}'=\frac{7}{8}x^{\frac{7}{8}-1}= \end{equation} \begin{equation} =\frac{7}{8}x^{-\frac{1}{8}}=\frac{7}{8\sqrt[8]{x}}; \end{equation} \begin{equation} 3){y}'={\left ( \frac{1}{\sqrt{x}} \right )}'= \end{equation} \begin{equation} ={\left ( x^{-\frac{1}{2}} \right )}'=-\frac{1}{2}x^{-\frac{1}{2}-1}= \end{equation} \begin{equation} =-\frac{1}{2}x^{-\frac{3}{2}}=-\frac{1}{2\sqrt[3]{x^{2}}}; \end{equation} \begin{equation} 4){y}'= {\left ( \frac{1}{\sqrt[8]{x^{5}}} \right )}'= \end{equation} \begin{equation} ={\left ( x^{-\frac{5}{8}} \right )}'=-\frac{5}{8}x^{-\frac{5}{8}-1}= \end{equation} \begin{equation} =-\frac{5}{8}x^{-\frac{13}{8}}=-\frac{5}{8\sqrt[8]{x^{18}}}. \end{equation}
\begin{equation} 1){y}'= {\left ( \sqrt[4]{x} \right )}'=\frac{1}{4\sqrt[4]{x^{3}}}; \end{equation} \begin{equation} 2){y}'={\left ( \sqrt[8]{x^{7}} \right )}'= \end{equation} \begin{equation} ={\left ( x^{\frac{7}{8}} \right )}'=\frac{7}{8}x^{\frac{7}{8}-1}= \end{equation} \begin{equation} =\frac{7}{8}x^{-\frac{1}{8}}=\frac{7}{8\sqrt[8]{x}}; \end{equation} \begin{equation} 3){y}'={\left ( \frac{1}{\sqrt{x}} \right )}'= \end{equation} \begin{equation} ={\left ( x^{-\frac{1}{2}} \right )}'=-\frac{1}{2}x^{-\frac{1}{2}-1}= \end{equation} \begin{equation} =-\frac{1}{2}x^{-\frac{3}{2}}=-\frac{1}{2\sqrt[3]{x^{2}}}; \end{equation} \begin{equation} 4){y}'= {\left ( \frac{1}{\sqrt[8]{x^{5}}} \right )}'= \end{equation} \begin{equation} ={\left ( x^{-\frac{5}{8}} \right )}'=-\frac{5}{8}x^{-\frac{5}{8}-1}= \end{equation} \begin{equation} =-\frac{5}{8}x^{-\frac{13}{8}}=-\frac{5}{8\sqrt[8]{x^{18}}}. \end{equation}