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

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