There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ \frac{({x}^{2} + 8{\frac{1}{x}}^{2} + 9)}{(1 + {x}^{2})}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{x^{2}}{(x^{2} + 1)} + \frac{8}{(x^{2} + 1)x^{2}} + \frac{9}{(x^{2} + 1)}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{x^{2}}{(x^{2} + 1)} + \frac{8}{(x^{2} + 1)x^{2}} + \frac{9}{(x^{2} + 1)}\right)}{dx}\\=&(\frac{-(2x + 0)}{(x^{2} + 1)^{2}})x^{2} + \frac{2x}{(x^{2} + 1)} + \frac{8(\frac{-(2x + 0)}{(x^{2} + 1)^{2}})}{x^{2}} + \frac{8*-2}{(x^{2} + 1)x^{3}} + 9(\frac{-(2x + 0)}{(x^{2} + 1)^{2}})\\=&\frac{-2x^{3}}{(x^{2} + 1)^{2}} + \frac{2x}{(x^{2} + 1)} - \frac{16}{(x^{2} + 1)^{2}x} - \frac{16}{(x^{2} + 1)x^{3}} - \frac{18x}{(x^{2} + 1)^{2}}\\ \end{split}\end{equation} \]

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