There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ 8ln(\frac{(sqrt({x}^{4} + 1) - 1)}{(sqrt({x}^{4} + 1) + 1)})\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = 8ln(\frac{sqrt(x^{4} + 1)}{(sqrt(x^{4} + 1) + 1)} - \frac{1}{(sqrt(x^{4} + 1) + 1)})\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( 8ln(\frac{sqrt(x^{4} + 1)}{(sqrt(x^{4} + 1) + 1)} - \frac{1}{(sqrt(x^{4} + 1) + 1)})\right)}{dx}\\=&\frac{8((\frac{-(\frac{(4x^{3} + 0)*\frac{1}{2}}{(x^{4} + 1)^{\frac{1}{2}}} + 0)}{(sqrt(x^{4} + 1) + 1)^{2}})sqrt(x^{4} + 1) + \frac{(4x^{3} + 0)*\frac{1}{2}}{(sqrt(x^{4} + 1) + 1)(x^{4} + 1)^{\frac{1}{2}}} - (\frac{-(\frac{(4x^{3} + 0)*\frac{1}{2}}{(x^{4} + 1)^{\frac{1}{2}}} + 0)}{(sqrt(x^{4} + 1) + 1)^{2}}))}{(\frac{sqrt(x^{4} + 1)}{(sqrt(x^{4} + 1) + 1)} - \frac{1}{(sqrt(x^{4} + 1) + 1)})}\\=&\frac{-16x^{3}sqrt(x^{4} + 1)}{(\frac{sqrt(x^{4} + 1)}{(sqrt(x^{4} + 1) + 1)} - \frac{1}{(sqrt(x^{4} + 1) + 1)})(sqrt(x^{4} + 1) + 1)^{2}(x^{4} + 1)^{\frac{1}{2}}} + \frac{16x^{3}}{(sqrt(x^{4} + 1) + 1)(\frac{sqrt(x^{4} + 1)}{(sqrt(x^{4} + 1) + 1)} - \frac{1}{(sqrt(x^{4} + 1) + 1)})(x^{4} + 1)^{\frac{1}{2}}} + \frac{16x^{3}}{(\frac{sqrt(x^{4} + 1)}{(sqrt(x^{4} + 1) + 1)} - \frac{1}{(sqrt(x^{4} + 1) + 1)})(sqrt(x^{4} + 1) + 1)^{2}(x^{4} + 1)^{\frac{1}{2}}}\\ \end{split}\end{equation} \]

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