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

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