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

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