There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ ln(\frac{({x}^{2} - 2{({x}^{2} - 9)}^{\frac{1}{2}})}{({x}^{2} - 18)})\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = ln(\frac{x^{2}}{(x^{2} - 18)} - \frac{2(x^{2} - 9)^{\frac{1}{2}}}{(x^{2} - 18)})\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( ln(\frac{x^{2}}{(x^{2} - 18)} - \frac{2(x^{2} - 9)^{\frac{1}{2}}}{(x^{2} - 18)})\right)}{dx}\\=&\frac{((\frac{-(2x + 0)}{(x^{2} - 18)^{2}})x^{2} + \frac{2x}{(x^{2} - 18)} - 2(\frac{-(2x + 0)}{(x^{2} - 18)^{2}})(x^{2} - 9)^{\frac{1}{2}} - \frac{2(\frac{\frac{1}{2}(2x + 0)}{(x^{2} - 9)^{\frac{1}{2}}})}{(x^{2} - 18)})}{(\frac{x^{2}}{(x^{2} - 18)} - \frac{2(x^{2} - 9)^{\frac{1}{2}}}{(x^{2} - 18)})}\\=&\frac{-2x^{3}}{(\frac{x^{2}}{(x^{2} - 18)} - \frac{2(x^{2} - 9)^{\frac{1}{2}}}{(x^{2} - 18)})(x^{2} - 18)^{2}} + \frac{2x}{(x^{2} - 18)(\frac{x^{2}}{(x^{2} - 18)} - \frac{2(x^{2} - 9)^{\frac{1}{2}}}{(x^{2} - 18)})} + \frac{4(x^{2} - 9)^{\frac{1}{2}}x}{(\frac{x^{2}}{(x^{2} - 18)} - \frac{2(x^{2} - 9)^{\frac{1}{2}}}{(x^{2} - 18)})(x^{2} - 18)^{2}} - \frac{2x}{(x^{2} - 9)^{\frac{1}{2}}(x^{2} - 18)(\frac{x^{2}}{(x^{2} - 18)} - \frac{2(x^{2} - 9)^{\frac{1}{2}}}{(x^{2} - 18)})}\\ \end{split}\end{equation} \]

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