There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ In(\frac{x{({x}^{2} + 1)}^{2}}{sqrt(2{x}^{3} - 1)})\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{Inx^{5}}{sqrt(2x^{3} - 1)} + \frac{2Inx^{3}}{sqrt(2x^{3} - 1)} + \frac{Inx}{sqrt(2x^{3} - 1)}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{Inx^{5}}{sqrt(2x^{3} - 1)} + \frac{2Inx^{3}}{sqrt(2x^{3} - 1)} + \frac{Inx}{sqrt(2x^{3} - 1)}\right)}{dx}\\=&\frac{In*5x^{4}}{sqrt(2x^{3} - 1)} + \frac{Inx^{5}*-(2*3x^{2} + 0)*\frac{1}{2}}{(2x^{3} - 1)(2x^{3} - 1)^{\frac{1}{2}}} + \frac{2In*3x^{2}}{sqrt(2x^{3} - 1)} + \frac{2Inx^{3}*-(2*3x^{2} + 0)*\frac{1}{2}}{(2x^{3} - 1)(2x^{3} - 1)^{\frac{1}{2}}} + \frac{In}{sqrt(2x^{3} - 1)} + \frac{Inx*-(2*3x^{2} + 0)*\frac{1}{2}}{(2x^{3} - 1)(2x^{3} - 1)^{\frac{1}{2}}}\\=&\frac{5Inx^{4}}{sqrt(2x^{3} - 1)} - \frac{3Inx^{7}}{(2x^{3} - 1)^{\frac{3}{2}}} + \frac{6Inx^{2}}{sqrt(2x^{3} - 1)} - \frac{6Inx^{5}}{(2x^{3} - 1)^{\frac{3}{2}}} + \frac{In}{sqrt(2x^{3} - 1)} - \frac{3Inx^{3}}{(2x^{3} - 1)^{\frac{3}{2}}}\\ \end{split}\end{equation} \]

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