There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ \frac{({x}^{3} - {x}^{8})}{({x}^{2} + {x}^{6})}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{x^{3}}{(x^{2} + x^{6})} - \frac{x^{8}}{(x^{2} + x^{6})}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{x^{3}}{(x^{2} + x^{6})} - \frac{x^{8}}{(x^{2} + x^{6})}\right)}{dx}\\=&(\frac{-(2x + 6x^{5})}{(x^{2} + x^{6})^{2}})x^{3} + \frac{3x^{2}}{(x^{2} + x^{6})} - (\frac{-(2x + 6x^{5})}{(x^{2} + x^{6})^{2}})x^{8} - \frac{8x^{7}}{(x^{2} + x^{6})}\\=&\frac{-2x^{4}}{(x^{2} + x^{6})^{2}} - \frac{6x^{8}}{(x^{2} + x^{6})^{2}} + \frac{3x^{2}}{(x^{2} + x^{6})} + \frac{2x^{9}}{(x^{2} + x^{6})^{2}} + \frac{6x^{13}}{(x^{2} + x^{6})^{2}} - \frac{8x^{7}}{(x^{2} + x^{6})}\\ \end{split}\end{equation} \]

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