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

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