There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ \frac{(-141sin(\frac{3}{2}x) - 10)}{(193 + 94cos(\frac{3}{2}x))}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{-141sin(\frac{3}{2}x)}{(94cos(\frac{3}{2}x) + 193)} - \frac{10}{(94cos(\frac{3}{2}x) + 193)}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{-141sin(\frac{3}{2}x)}{(94cos(\frac{3}{2}x) + 193)} - \frac{10}{(94cos(\frac{3}{2}x) + 193)}\right)}{dx}\\=&-141(\frac{-(94*-sin(\frac{3}{2}x)*\frac{3}{2} + 0)}{(94cos(\frac{3}{2}x) + 193)^{2}})sin(\frac{3}{2}x) - \frac{141cos(\frac{3}{2}x)*\frac{3}{2}}{(94cos(\frac{3}{2}x) + 193)} - 10(\frac{-(94*-sin(\frac{3}{2}x)*\frac{3}{2} + 0)}{(94cos(\frac{3}{2}x) + 193)^{2}})\\=&\frac{-19881sin^{2}(\frac{3}{2}x)}{(94cos(\frac{3}{2}x) + 193)^{2}} - \frac{423cos(\frac{3}{2}x)}{2(94cos(\frac{3}{2}x) + 193)} - \frac{1410sin(\frac{3}{2}x)}{(94cos(\frac{3}{2}x) + 193)^{2}}\\ \end{split}\end{equation} \]

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