There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ arccos(\frac{5cos(x)}{sqrt(169 + 120sin(x))})\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = arccos(\frac{5cos(x)}{sqrt(120sin(x) + 169)})\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( arccos(\frac{5cos(x)}{sqrt(120sin(x) + 169)})\right)}{dx}\\=&(\frac{-(\frac{5*-sin(x)}{sqrt(120sin(x) + 169)} + \frac{5cos(x)*-(120cos(x) + 0)*\frac{1}{2}}{(120sin(x) + 169)(120sin(x) + 169)^{\frac{1}{2}}})}{((1 - (\frac{5cos(x)}{sqrt(120sin(x) + 169)})^{2})^{\frac{1}{2}})})\\=&\frac{5sin(x)}{(\frac{-25cos^{2}(x)}{sqrt(120sin(x) + 169)^{2}} + 1)^{\frac{1}{2}}sqrt(120sin(x) + 169)} + \frac{300cos^{2}(x)}{(\frac{-25cos^{2}(x)}{sqrt(120sin(x) + 169)^{2}} + 1)^{\frac{1}{2}}(120sin(x) + 169)^{\frac{3}{2}}}\\ \end{split}\end{equation} \]

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