There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ \frac{(5x + sin(x))}{(3x - sin(x))}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{5x}{(3x - sin(x))} + \frac{sin(x)}{(3x - sin(x))}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{5x}{(3x - sin(x))} + \frac{sin(x)}{(3x - sin(x))}\right)}{dx}\\=&5(\frac{-(3 - cos(x))}{(3x - sin(x))^{2}})x + \frac{5}{(3x - sin(x))} + (\frac{-(3 - cos(x))}{(3x - sin(x))^{2}})sin(x) + \frac{cos(x)}{(3x - sin(x))}\\=&\frac{5xcos(x)}{(3x - sin(x))^{2}} - \frac{15x}{(3x - sin(x))^{2}} + \frac{cos(x)}{(3x - sin(x))} + \frac{sin(x)cos(x)}{(3x - sin(x))^{2}} - \frac{3sin(x)}{(3x - sin(x))^{2}} + \frac{5}{(3x - sin(x))}\\ \end{split}\end{equation} \]

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