There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ {x}^{8}{(x - 9)}^{3}{\frac{1}{({x}^{2} + 8)}}^{3}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{x^{11}}{(x^{2} + 8)^{3}} - \frac{27x^{10}}{(x^{2} + 8)^{3}} + \frac{243x^{9}}{(x^{2} + 8)^{3}} - \frac{729x^{8}}{(x^{2} + 8)^{3}}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{x^{11}}{(x^{2} + 8)^{3}} - \frac{27x^{10}}{(x^{2} + 8)^{3}} + \frac{243x^{9}}{(x^{2} + 8)^{3}} - \frac{729x^{8}}{(x^{2} + 8)^{3}}\right)}{dx}\\=&(\frac{-3(2x + 0)}{(x^{2} + 8)^{4}})x^{11} + \frac{11x^{10}}{(x^{2} + 8)^{3}} - 27(\frac{-3(2x + 0)}{(x^{2} + 8)^{4}})x^{10} - \frac{27*10x^{9}}{(x^{2} + 8)^{3}} + 243(\frac{-3(2x + 0)}{(x^{2} + 8)^{4}})x^{9} + \frac{243*9x^{8}}{(x^{2} + 8)^{3}} - 729(\frac{-3(2x + 0)}{(x^{2} + 8)^{4}})x^{8} - \frac{729*8x^{7}}{(x^{2} + 8)^{3}}\\=&\frac{-6x^{12}}{(x^{2} + 8)^{4}} + \frac{11x^{10}}{(x^{2} + 8)^{3}} + \frac{162x^{11}}{(x^{2} + 8)^{4}} - \frac{270x^{9}}{(x^{2} + 8)^{3}} - \frac{1458x^{10}}{(x^{2} + 8)^{4}} + \frac{2187x^{8}}{(x^{2} + 8)^{3}} + \frac{4374x^{9}}{(x^{2} + 8)^{4}} - \frac{5832x^{7}}{(x^{2} + 8)^{3}}\\ \end{split}\end{equation} \]

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