There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ \frac{((-3xx + 12x)(12x - 8) - 12(6xx - xxx))(6xx - xxx)}{(6xx - xxx)}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{-240x^{5}}{(-x^{3} + 6x^{2})} + \frac{24x^{6}}{(-x^{3} + 6x^{2})} + \frac{672x^{4}}{(-x^{3} + 6x^{2})} - \frac{576x^{3}}{(-x^{3} + 6x^{2})}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{-240x^{5}}{(-x^{3} + 6x^{2})} + \frac{24x^{6}}{(-x^{3} + 6x^{2})} + \frac{672x^{4}}{(-x^{3} + 6x^{2})} - \frac{576x^{3}}{(-x^{3} + 6x^{2})}\right)}{dx}\\=&-240(\frac{-(-3x^{2} + 6*2x)}{(-x^{3} + 6x^{2})^{2}})x^{5} - \frac{240*5x^{4}}{(-x^{3} + 6x^{2})} + 24(\frac{-(-3x^{2} + 6*2x)}{(-x^{3} + 6x^{2})^{2}})x^{6} + \frac{24*6x^{5}}{(-x^{3} + 6x^{2})} + 672(\frac{-(-3x^{2} + 6*2x)}{(-x^{3} + 6x^{2})^{2}})x^{4} + \frac{672*4x^{3}}{(-x^{3} + 6x^{2})} - 576(\frac{-(-3x^{2} + 6*2x)}{(-x^{3} + 6x^{2})^{2}})x^{3} - \frac{576*3x^{2}}{(-x^{3} + 6x^{2})}\\=&\frac{-1008x^{7}}{(-x^{3} + 6x^{2})^{2}} + \frac{4896x^{6}}{(-x^{3} + 6x^{2})^{2}} - \frac{1200x^{4}}{(-x^{3} + 6x^{2})} + \frac{72x^{8}}{(-x^{3} + 6x^{2})^{2}} + \frac{144x^{5}}{(-x^{3} + 6x^{2})} - \frac{9792x^{5}}{(-x^{3} + 6x^{2})^{2}} + \frac{2688x^{3}}{(-x^{3} + 6x^{2})} + \frac{6912x^{4}}{(-x^{3} + 6x^{2})^{2}} - \frac{1728x^{2}}{(-x^{3} + 6x^{2})}\\ \end{split}\end{equation} \]

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