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

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