There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ 1 + \frac{\frac{4}{5}}{(1 + {(\frac{x}{\frac{19}{5}})}^{\frac{16}{5}})}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{\frac{4}{5}}{(\frac{x^{\frac{16}{5}}}{\frac{19}{5}^{\frac{16}{5}}} + 1)} + 1\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{\frac{4}{5}}{(\frac{x^{\frac{16}{5}}}{\frac{19}{5}^{\frac{16}{5}}} + 1)} + 1\right)}{dx}\\=&\frac{4}{5}(\frac{-(\frac{\frac{16}{5}x^{\frac{11}{5}}}{\frac{19}{5}^{\frac{16}{5}}} + 0)}{(\frac{x^{\frac{16}{5}}}{\frac{19}{5}^{\frac{16}{5}}} + 1)^{2}}) + 0\\=& - \frac{64*5^{\frac{16}{5}}x^{\frac{11}{5}}}{25*19^{\frac{16}{5}}(\frac{x^{\frac{16}{5}}}{\frac{19}{5}^{\frac{16}{5}}} + 1)^{2}}\\ \end{split}\end{equation} \]

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