There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ -ln(\frac{1}{(1 + e^{999(25 - x)})})\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = -ln(\frac{1}{(e^{-999x + 24975} + 1)})\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( -ln(\frac{1}{(e^{-999x + 24975} + 1)})\right)}{dx}\\=&\frac{-(\frac{-(e^{-999x + 24975}(-999 + 0) + 0)}{(e^{-999x + 24975} + 1)^{2}})}{(\frac{1}{(e^{-999x + 24975} + 1)})}\\=&\frac{-999e^{-999x + 24975}}{(e^{-999x + 24975} + 1)}\\ \end{split}\end{equation} \]

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