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

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