There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ arctan(\frac{(4sin(x))}{(3 + 5cos(x))})\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = arctan(\frac{4sin(x)}{(5cos(x) + 3)})\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( arctan(\frac{4sin(x)}{(5cos(x) + 3)})\right)}{dx}\\=&(\frac{(4(\frac{-(5*-sin(x) + 0)}{(5cos(x) + 3)^{2}})sin(x) + \frac{4cos(x)}{(5cos(x) + 3)})}{(1 + (\frac{4sin(x)}{(5cos(x) + 3)})^{2})})\\=&\frac{20sin^{2}(x)}{(5cos(x) + 3)^{2}(\frac{16sin^{2}(x)}{(5cos(x) + 3)^{2}} + 1)} + \frac{4cos(x)}{(5cos(x) + 3)(\frac{16sin^{2}(x)}{(5cos(x) + 3)^{2}} + 1)}\\ \end{split}\end{equation} \]

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