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

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