There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ {ln(1 - \frac{cos(x)}{(1 + cos(t))})}^{4}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = ln^{4}(\frac{-cos(x)}{(cos(t) + 1)} + 1)\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( ln^{4}(\frac{-cos(x)}{(cos(t) + 1)} + 1)\right)}{dx}\\=&\frac{4ln^{3}(\frac{-cos(x)}{(cos(t) + 1)} + 1)(-(\frac{-(-sin(t)*0 + 0)}{(cos(t) + 1)^{2}})cos(x) - \frac{-sin(x)}{(cos(t) + 1)} + 0)}{(\frac{-cos(x)}{(cos(t) + 1)} + 1)}\\=&\frac{4ln^{3}(\frac{-cos(x)}{(cos(t) + 1)} + 1)sin(x)}{(\frac{-cos(x)}{(cos(t) + 1)} + 1)(cos(t) + 1)}\\ \end{split}\end{equation} \]

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