There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ \frac{(6 + 2cos(x))}{(1 - {cos(x)}^{2})}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{2cos(x)}{(-cos^{2}(x) + 1)} + \frac{6}{(-cos^{2}(x) + 1)}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{2cos(x)}{(-cos^{2}(x) + 1)} + \frac{6}{(-cos^{2}(x) + 1)}\right)}{dx}\\=&2(\frac{-(--2cos(x)sin(x) + 0)}{(-cos^{2}(x) + 1)^{2}})cos(x) + \frac{2*-sin(x)}{(-cos^{2}(x) + 1)} + 6(\frac{-(--2cos(x)sin(x) + 0)}{(-cos^{2}(x) + 1)^{2}})\\=& - \frac{4sin(x)cos^{2}(x)}{(-cos^{2}(x) + 1)^{2}} - \frac{12sin(x)cos(x)}{(-cos^{2}(x) + 1)^{2}} - \frac{2sin(x)}{(-cos^{2}(x) + 1)}\\ \end{split}\end{equation} \]

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