There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ 10 * {\frac{27}{10}}^{(8 - x)}{\frac{1}{(1 + {\frac{27}{10}}^{(8 - x)})}}^{2}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{10 * {\frac{27}{10}}^{(-x + 8)}}{({\frac{27}{10}}^{(-x + 8)} + 1)^{2}}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{10 * {\frac{27}{10}}^{(-x + 8)}}{({\frac{27}{10}}^{(-x + 8)} + 1)^{2}}\right)}{dx}\\=&10(\frac{-2(({\frac{27}{10}}^{(-x + 8)}((-1 + 0)ln(\frac{27}{10}) + \frac{(-x + 8)(0)}{(\frac{27}{10})})) + 0)}{({\frac{27}{10}}^{(-x + 8)} + 1)^{3}}){\frac{27}{10}}^{(-x + 8)} + \frac{10({\frac{27}{10}}^{(-x + 8)}((-1 + 0)ln(\frac{27}{10}) + \frac{(-x + 8)(0)}{(\frac{27}{10})}))}{({\frac{27}{10}}^{(-x + 8)} + 1)^{2}}\\=&\frac{20 * {\frac{27}{10}}^{(-2x + 16)}ln(\frac{27}{10})}{({\frac{27}{10}}^{(-x + 8)} + 1)^{3}} - \frac{10 * {\frac{27}{10}}^{(-x + 8)}ln(\frac{27}{10})}{({\frac{27}{10}}^{(-x + 8)} + 1)^{2}}\\ \end{split}\end{equation} \]

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