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

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