There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
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\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ {(\frac{({x}^{3} - 2x + 1)}{({x}^{2} - 7)})}^{x}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = (\frac{x^{3}}{(x^{2} - 7)} - \frac{2x}{(x^{2} - 7)} + \frac{1}{(x^{2} - 7)})^{x}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( (\frac{x^{3}}{(x^{2} - 7)} - \frac{2x}{(x^{2} - 7)} + \frac{1}{(x^{2} - 7)})^{x}\right)}{dx}\\=&((\frac{x^{3}}{(x^{2} - 7)} - \frac{2x}{(x^{2} - 7)} + \frac{1}{(x^{2} - 7)})^{x}((1)ln(\frac{x^{3}}{(x^{2} - 7)} - \frac{2x}{(x^{2} - 7)} + \frac{1}{(x^{2} - 7)}) + \frac{(x)((\frac{-(2x + 0)}{(x^{2} - 7)^{2}})x^{3} + \frac{3x^{2}}{(x^{2} - 7)} - 2(\frac{-(2x + 0)}{(x^{2} - 7)^{2}})x - \frac{2}{(x^{2} - 7)} + (\frac{-(2x + 0)}{(x^{2} - 7)^{2}}))}{(\frac{x^{3}}{(x^{2} - 7)} - \frac{2x}{(x^{2} - 7)} + \frac{1}{(x^{2} - 7)})}))\\=&(\frac{x^{3}}{(x^{2} - 7)} - \frac{2x}{(x^{2} - 7)} + \frac{1}{(x^{2} - 7)})^{x}ln(\frac{x^{3}}{(x^{2} - 7)} - \frac{2x}{(x^{2} - 7)} + \frac{1}{(x^{2} - 7)}) - \frac{2x^{5}(\frac{x^{3}}{(x^{2} - 7)} - \frac{2x}{(x^{2} - 7)} + \frac{1}{(x^{2} - 7)})^{x}}{(x^{2} - 7)^{2}(\frac{x^{3}}{(x^{2} - 7)} - \frac{2x}{(x^{2} - 7)} + \frac{1}{(x^{2} - 7)})} + \frac{3x^{3}(\frac{x^{3}}{(x^{2} - 7)} - \frac{2x}{(x^{2} - 7)} + \frac{1}{(x^{2} - 7)})^{x}}{(x^{2} - 7)(\frac{x^{3}}{(x^{2} - 7)} - \frac{2x}{(x^{2} - 7)} + \frac{1}{(x^{2} - 7)})} + \frac{4x^{3}(\frac{x^{3}}{(x^{2} - 7)} - \frac{2x}{(x^{2} - 7)} + \frac{1}{(x^{2} - 7)})^{x}}{(x^{2} - 7)^{2}(\frac{x^{3}}{(x^{2} - 7)} - \frac{2x}{(x^{2} - 7)} + \frac{1}{(x^{2} - 7)})} - \frac{2x(\frac{x^{3}}{(x^{2} - 7)} - \frac{2x}{(x^{2} - 7)} + \frac{1}{(x^{2} - 7)})^{x}}{(x^{2} - 7)(\frac{x^{3}}{(x^{2} - 7)} - \frac{2x}{(x^{2} - 7)} + \frac{1}{(x^{2} - 7)})} - \frac{2x^{2}(\frac{x^{3}}{(x^{2} - 7)} - \frac{2x}{(x^{2} - 7)} + \frac{1}{(x^{2} - 7)})^{x}}{(x^{2} - 7)^{2}(\frac{x^{3}}{(x^{2} - 7)} - \frac{2x}{(x^{2} - 7)} + \frac{1}{(x^{2} - 7)})}\\ \end{split}\end{equation} \]

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