本次共计算 1 个题目：每一题对 x 求 2 阶导数。
    注意，变量是区分大小写的。
\[ \begin{equation}\begin{split}【1/1】求函数\frac{(1 - csc(x))}{(1 + csc(x))} 关于 x 的 2 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = - \frac{csc(x)}{(csc(x) + 1)} + \frac{1}{(csc(x) + 1)}\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( - \frac{csc(x)}{(csc(x) + 1)} + \frac{1}{(csc(x) + 1)}\right)}{dx}\\=& - (\frac{-(-csc(x)cot(x) + 0)}{(csc(x) + 1)^{2}})csc(x) - \frac{-csc(x)cot(x)}{(csc(x) + 1)} + (\frac{-(-csc(x)cot(x) + 0)}{(csc(x) + 1)^{2}})\\=& - \frac{cot(x)csc^{2}(x)}{(csc(x) + 1)^{2}} + \frac{cot(x)csc(x)}{(csc(x) + 1)} + \frac{cot(x)csc(x)}{(csc(x) + 1)^{2}}\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( - \frac{cot(x)csc^{2}(x)}{(csc(x) + 1)^{2}} + \frac{cot(x)csc(x)}{(csc(x) + 1)} + \frac{cot(x)csc(x)}{(csc(x) + 1)^{2}}\right)}{dx}\\=& - (\frac{-2(-csc(x)cot(x) + 0)}{(csc(x) + 1)^{3}})cot(x)csc^{2}(x) - \frac{-csc^{2}(x)csc^{2}(x)}{(csc(x) + 1)^{2}} - \frac{cot(x)*-2csc^{2}(x)cot(x)}{(csc(x) + 1)^{2}} + (\frac{-(-csc(x)cot(x) + 0)}{(csc(x) + 1)^{2}})cot(x)csc(x) + \frac{-csc^{2}(x)csc(x)}{(csc(x) + 1)} + \frac{cot(x)*-csc(x)cot(x)}{(csc(x) + 1)} + (\frac{-2(-csc(x)cot(x) + 0)}{(csc(x) + 1)^{3}})cot(x)csc(x) + \frac{-csc^{2}(x)csc(x)}{(csc(x) + 1)^{2}} + \frac{cot(x)*-csc(x)cot(x)}{(csc(x) + 1)^{2}}\\=& - \frac{2cot^{2}(x)csc^{3}(x)}{(csc(x) + 1)^{3}} + \frac{csc^{4}(x)}{(csc(x) + 1)^{2}} + \frac{3cot^{2}(x)csc^{2}(x)}{(csc(x) + 1)^{2}} - \frac{csc^{3}(x)}{(csc(x) + 1)} - \frac{cot^{2}(x)csc(x)}{(csc(x) + 1)} + \frac{2cot^{2}(x)csc^{2}(x)}{(csc(x) + 1)^{3}} - \frac{csc^{3}(x)}{(csc(x) + 1)^{2}} - \frac{cot^{2}(x)csc(x)}{(csc(x) + 1)^{2}}\\ \end{split}\end{equation} \]

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