There are 1 questions in this calculation: for each question, the 2 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ second\ derivative\ of\ function\ \frac{cos(x)}{2} - \frac{ln(cot(x) + csc(x))}{2}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{1}{2}cos(x) - \frac{1}{2}ln(cot(x) + csc(x))\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{1}{2}cos(x) - \frac{1}{2}ln(cot(x) + csc(x))\right)}{dx}\\=&\frac{1}{2}*-sin(x) - \frac{\frac{1}{2}(-csc^{2}(x) + -csc(x)cot(x))}{(cot(x) + csc(x))}\\=&\frac{-sin(x)}{2} + \frac{csc^{2}(x)}{2(cot(x) + csc(x))} + \frac{cot(x)csc(x)}{2(cot(x) + csc(x))}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{-sin(x)}{2} + \frac{csc^{2}(x)}{2(cot(x) + csc(x))} + \frac{cot(x)csc(x)}{2(cot(x) + csc(x))}\right)}{dx}\\=&\frac{-cos(x)}{2} + \frac{(\frac{-(-csc^{2}(x) + -csc(x)cot(x))}{(cot(x) + csc(x))^{2}})csc^{2}(x)}{2} + \frac{-2csc^{2}(x)cot(x)}{2(cot(x) + csc(x))} + \frac{(\frac{-(-csc^{2}(x) + -csc(x)cot(x))}{(cot(x) + csc(x))^{2}})cot(x)csc(x)}{2} + \frac{-csc^{2}(x)csc(x)}{2(cot(x) + csc(x))} + \frac{cot(x)*-csc(x)cot(x)}{2(cot(x) + csc(x))}\\=&\frac{-cos(x)}{2} + \frac{csc^{4}(x)}{2(cot(x) + csc(x))^{2}} + \frac{cot(x)csc^{3}(x)}{(cot(x) + csc(x))^{2}} - \frac{cot(x)csc^{2}(x)}{(cot(x) + csc(x))} + \frac{cot^{2}(x)csc^{2}(x)}{2(cot(x) + csc(x))^{2}} - \frac{csc^{3}(x)}{2(cot(x) + csc(x))} - \frac{cot^{2}(x)csc(x)}{2(cot(x) + csc(x))}\\ \end{split}\end{equation} \]

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