There are 1 questions in this calculation: for each question, the 3 derivative of x is calculated.
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\[ \begin{equation}\begin{split}[1/1]Find\ the\ third\ derivative\ of\ function\ \frac{(-84{x}^{2} - 98x + 61)}{(-65x - 69)}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{-84x^{2}}{(-65x - 69)} - \frac{98x}{(-65x - 69)} + \frac{61}{(-65x - 69)}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{-84x^{2}}{(-65x - 69)} - \frac{98x}{(-65x - 69)} + \frac{61}{(-65x - 69)}\right)}{dx}\\=&-84(\frac{-(-65 + 0)}{(-65x - 69)^{2}})x^{2} - \frac{84*2x}{(-65x - 69)} - 98(\frac{-(-65 + 0)}{(-65x - 69)^{2}})x - \frac{98}{(-65x - 69)} + 61(\frac{-(-65 + 0)}{(-65x - 69)^{2}})\\=&\frac{-5460x^{2}}{(-65x - 69)^{2}} - \frac{168x}{(-65x - 69)} - \frac{6370x}{(-65x - 69)^{2}} + \frac{3965}{(-65x - 69)^{2}} - \frac{98}{(-65x - 69)}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{-5460x^{2}}{(-65x - 69)^{2}} - \frac{168x}{(-65x - 69)} - \frac{6370x}{(-65x - 69)^{2}} + \frac{3965}{(-65x - 69)^{2}} - \frac{98}{(-65x - 69)}\right)}{dx}\\=&-5460(\frac{-2(-65 + 0)}{(-65x - 69)^{3}})x^{2} - \frac{5460*2x}{(-65x - 69)^{2}} - 168(\frac{-(-65 + 0)}{(-65x - 69)^{2}})x - \frac{168}{(-65x - 69)} - 6370(\frac{-2(-65 + 0)}{(-65x - 69)^{3}})x - \frac{6370}{(-65x - 69)^{2}} + 3965(\frac{-2(-65 + 0)}{(-65x - 69)^{3}}) - 98(\frac{-(-65 + 0)}{(-65x - 69)^{2}})\\=&\frac{-709800x^{2}}{(-65x - 69)^{3}} - \frac{21840x}{(-65x - 69)^{2}} - \frac{828100x}{(-65x - 69)^{3}} + \frac{515450}{(-65x - 69)^{3}} - \frac{12740}{(-65x - 69)^{2}} - \frac{168}{(-65x - 69)}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( \frac{-709800x^{2}}{(-65x - 69)^{3}} - \frac{21840x}{(-65x - 69)^{2}} - \frac{828100x}{(-65x - 69)^{3}} + \frac{515450}{(-65x - 69)^{3}} - \frac{12740}{(-65x - 69)^{2}} - \frac{168}{(-65x - 69)}\right)}{dx}\\=&-709800(\frac{-3(-65 + 0)}{(-65x - 69)^{4}})x^{2} - \frac{709800*2x}{(-65x - 69)^{3}} - 21840(\frac{-2(-65 + 0)}{(-65x - 69)^{3}})x - \frac{21840}{(-65x - 69)^{2}} - 828100(\frac{-3(-65 + 0)}{(-65x - 69)^{4}})x - \frac{828100}{(-65x - 69)^{3}} + 515450(\frac{-3(-65 + 0)}{(-65x - 69)^{4}}) - 12740(\frac{-2(-65 + 0)}{(-65x - 69)^{3}}) - 168(\frac{-(-65 + 0)}{(-65x - 69)^{2}})\\=&\frac{-138411000x^{2}}{(-65x - 69)^{4}} - \frac{4258800x}{(-65x - 69)^{3}} - \frac{161479500x}{(-65x - 69)^{4}} + \frac{100512750}{(-65x - 69)^{4}} - \frac{2484300}{(-65x - 69)^{3}} - \frac{32760}{(-65x - 69)^{2}}\\ \end{split}\end{equation} \]

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