There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ ln(1 + cos(x))*0.125 + \frac{0.25}{(1 + cos(x) + 0.125ln(1 - cos(x)))}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = 0.125ln(cos(x) + 1) + \frac{0.25}{(cos(x) + 0.125ln(-cos(x) + 1) + 1)}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( 0.125ln(cos(x) + 1) + \frac{0.25}{(cos(x) + 0.125ln(-cos(x) + 1) + 1)}\right)}{dx}\\=&\frac{0.125(-sin(x) + 0)}{(cos(x) + 1)} + 0.25(\frac{-(-sin(x) + \frac{0.125(--sin(x) + 0)}{(-cos(x) + 1)} + 0)}{(cos(x) + 0.125ln(-cos(x) + 1) + 1)^{2}})\\=&\frac{-0.125sin(x)}{(cos(x) + 1)} + \frac{0.25sin(x)}{(cos(x) + 0.125ln(-cos(x) + 1) + 1)(cos(x) + 0.125ln(-cos(x) + 1) + 1)} - \frac{0.03125sin(x)}{(cos(x) + 0.125ln(-cos(x) + 1) + 1)(cos(x) + 0.125ln(-cos(x) + 1) + 1)(-cos(x) + 1)}\\ \end{split}\end{equation} \]

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