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

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