There are 1 questions in this calculation: for each question, the 1 derivative of n is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ \frac{({n}^{4} - n)}{((1 - n)*5{n}^{(\frac{9}{2})})}\ with\ respect\ to\ n：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{n^{4}}{(-5n^{\frac{11}{2}} + 5n^{\frac{9}{2}})} - \frac{n}{(-5n^{\frac{11}{2}} + 5n^{\frac{9}{2}})}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{n^{4}}{(-5n^{\frac{11}{2}} + 5n^{\frac{9}{2}})} - \frac{n}{(-5n^{\frac{11}{2}} + 5n^{\frac{9}{2}})}\right)}{dn}\\=&(\frac{-(-5*\frac{11}{2}n^{\frac{9}{2}} + 5*\frac{9}{2}n^{\frac{7}{2}})}{(-5n^{\frac{11}{2}} + 5n^{\frac{9}{2}})^{2}})n^{4} + \frac{4n^{3}}{(-5n^{\frac{11}{2}} + 5n^{\frac{9}{2}})} - (\frac{-(-5*\frac{11}{2}n^{\frac{9}{2}} + 5*\frac{9}{2}n^{\frac{7}{2}})}{(-5n^{\frac{11}{2}} + 5n^{\frac{9}{2}})^{2}})n - \frac{1}{(-5n^{\frac{11}{2}} + 5n^{\frac{9}{2}})}\\=&\frac{55n^{\frac{17}{2}}}{2(-5n^{\frac{11}{2}} + 5n^{\frac{9}{2}})^{2}} - \frac{45n^{\frac{15}{2}}}{2(-5n^{\frac{11}{2}} + 5n^{\frac{9}{2}})^{2}} + \frac{4n^{3}}{(-5n^{\frac{11}{2}} + 5n^{\frac{9}{2}})} - \frac{55n^{\frac{11}{2}}}{2(-5n^{\frac{11}{2}} + 5n^{\frac{9}{2}})^{2}} + \frac{45n^{\frac{9}{2}}}{2(-5n^{\frac{11}{2}} + 5n^{\frac{9}{2}})^{2}} - \frac{1}{(-5n^{\frac{11}{2}} + 5n^{\frac{9}{2}})}\\ \end{split}\end{equation} \]

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