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

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