There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ -20cos(x){\frac{1}{(4sin(x) + 5)}}^{2}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{-20cos(x)}{(4sin(x) + 5)^{2}}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{-20cos(x)}{(4sin(x) + 5)^{2}}\right)}{dx}\\=&-20(\frac{-2(4cos(x) + 0)}{(4sin(x) + 5)^{3}})cos(x) - \frac{20*-sin(x)}{(4sin(x) + 5)^{2}}\\=&\frac{160cos^{2}(x)}{(4sin(x) + 5)^{3}} + \frac{20sin(x)}{(4sin(x) + 5)^{2}}\\ \end{split}\end{equation} \]

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