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

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