There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ \frac{(5 - cos(x))}{(5 + sin(x))}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = - \frac{cos(x)}{(sin(x) + 5)} + \frac{5}{(sin(x) + 5)}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( - \frac{cos(x)}{(sin(x) + 5)} + \frac{5}{(sin(x) + 5)}\right)}{dx}\\=& - (\frac{-(cos(x) + 0)}{(sin(x) + 5)^{2}})cos(x) - \frac{-sin(x)}{(sin(x) + 5)} + 5(\frac{-(cos(x) + 0)}{(sin(x) + 5)^{2}})\\=&\frac{cos^{2}(x)}{(sin(x) + 5)^{2}} + \frac{sin(x)}{(sin(x) + 5)} - \frac{5cos(x)}{(sin(x) + 5)^{2}}\\ \end{split}\end{equation} \]

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