There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ log_{100}^{\frac{(1 + {100}^{(x - 1)})}{(1 + {100}^{(-x - 1)})}}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = log_{100}^{\frac{{100}^{(x - 1)}}{({100}^{(-x - 1)} + 1)} + \frac{1}{({100}^{(-x - 1)} + 1)}}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( log_{100}^{\frac{{100}^{(x - 1)}}{({100}^{(-x - 1)} + 1)} + \frac{1}{({100}^{(-x - 1)} + 1)}}\right)}{dx}\\=&(\frac{(\frac{((\frac{-(({100}^{(-x - 1)}((-1 + 0)ln(100) + \frac{(-x - 1)(0)}{(100)})) + 0)}{({100}^{(-x - 1)} + 1)^{2}}){100}^{(x - 1)} + \frac{({100}^{(x - 1)}((1 + 0)ln(100) + \frac{(x - 1)(0)}{(100)}))}{({100}^{(-x - 1)} + 1)} + (\frac{-(({100}^{(-x - 1)}((-1 + 0)ln(100) + \frac{(-x - 1)(0)}{(100)})) + 0)}{({100}^{(-x - 1)} + 1)^{2}}))}{(\frac{{100}^{(x - 1)}}{({100}^{(-x - 1)} + 1)} + \frac{1}{({100}^{(-x - 1)} + 1)})} - \frac{(0)log_{100}^{\frac{{100}^{(x - 1)}}{({100}^{(-x - 1)} + 1)} + \frac{1}{({100}^{(-x - 1)} + 1)}}}{(100)})}{(ln(100))})\\=&\frac{{100}^{(2x - 2)}}{({100}^{(-x - 1)} + 1)^{2}(\frac{{100}^{(x - 1)}}{({100}^{(-x - 1)} + 1)} + \frac{1}{({100}^{(-x - 1)} + 1)})} + \frac{{100}^{(x - 1)}}{({100}^{(-x - 1)} + 1)(\frac{{100}^{(x - 1)}}{({100}^{(-x - 1)} + 1)} + \frac{1}{({100}^{(-x - 1)} + 1)})} + \frac{{100}^{(-x - 1)}}{({100}^{(-x - 1)} + 1)^{2}(\frac{{100}^{(x - 1)}}{({100}^{(-x - 1)} + 1)} + \frac{1}{({100}^{(-x - 1)} + 1)})}\\ \end{split}\end{equation} \]

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