本次共计算 1 个题目：每一题对 n 求 1 阶导数。
    注意，变量是区分大小写的。
\[ \begin{equation}\begin{split}【1/1】求函数\frac{({n}^{4} - n)}{((1 - n)*5{n}^{(\frac{9}{2})})} 关于 n 的 1 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = \frac{n^{4}}{(-5n^{\frac{11}{2}} + 5n^{\frac{9}{2}})} - \frac{n}{(-5n^{\frac{11}{2}} + 5n^{\frac{9}{2}})}\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( \frac{n^{4}}{(-5n^{\frac{11}{2}} + 5n^{\frac{9}{2}})} - \frac{n}{(-5n^{\frac{11}{2}} + 5n^{\frac{9}{2}})}\right)}{dn}\\=&(\frac{-(-5*\frac{11}{2}n^{\frac{9}{2}} + 5*\frac{9}{2}n^{\frac{7}{2}})}{(-5n^{\frac{11}{2}} + 5n^{\frac{9}{2}})^{2}})n^{4} + \frac{4n^{3}}{(-5n^{\frac{11}{2}} + 5n^{\frac{9}{2}})} - (\frac{-(-5*\frac{11}{2}n^{\frac{9}{2}} + 5*\frac{9}{2}n^{\frac{7}{2}})}{(-5n^{\frac{11}{2}} + 5n^{\frac{9}{2}})^{2}})n - \frac{1}{(-5n^{\frac{11}{2}} + 5n^{\frac{9}{2}})}\\=&\frac{55n^{\frac{17}{2}}}{2(-5n^{\frac{11}{2}} + 5n^{\frac{9}{2}})^{2}} - \frac{45n^{\frac{15}{2}}}{2(-5n^{\frac{11}{2}} + 5n^{\frac{9}{2}})^{2}} + \frac{4n^{3}}{(-5n^{\frac{11}{2}} + 5n^{\frac{9}{2}})} - \frac{55n^{\frac{11}{2}}}{2(-5n^{\frac{11}{2}} + 5n^{\frac{9}{2}})^{2}} + \frac{45n^{\frac{9}{2}}}{2(-5n^{\frac{11}{2}} + 5n^{\frac{9}{2}})^{2}} - \frac{1}{(-5n^{\frac{11}{2}} + 5n^{\frac{9}{2}})}\\ \end{split}\end{equation} \]

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