There are 1 questions in this calculation: for each question, the 2 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ second\ derivative\ of\ function\ \frac{x}{sin(\frac{πx}{180})}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{x}{sin(\frac{1}{180}πx)}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{x}{sin(\frac{1}{180}πx)}\right)}{dx}\\=&\frac{1}{sin(\frac{1}{180}πx)} + \frac{x*-cos(\frac{1}{180}πx)*\frac{1}{180}π}{sin^{2}(\frac{1}{180}πx)}\\=&\frac{1}{sin(\frac{1}{180}πx)} - \frac{πxcos(\frac{1}{180}πx)}{180sin^{2}(\frac{1}{180}πx)}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{1}{sin(\frac{1}{180}πx)} - \frac{πxcos(\frac{1}{180}πx)}{180sin^{2}(\frac{1}{180}πx)}\right)}{dx}\\=&\frac{-cos(\frac{1}{180}πx)*\frac{1}{180}π}{sin^{2}(\frac{1}{180}πx)} - \frac{πcos(\frac{1}{180}πx)}{180sin^{2}(\frac{1}{180}πx)} - \frac{πx*-2cos(\frac{1}{180}πx)*\frac{1}{180}πcos(\frac{1}{180}πx)}{180sin^{3}(\frac{1}{180}πx)} - \frac{πx*-sin(\frac{1}{180}πx)*\frac{1}{180}π}{180sin^{2}(\frac{1}{180}πx)}\\=&\frac{-πcos(\frac{1}{180}πx)}{90sin^{2}(\frac{1}{180}πx)} + \frac{π^{2}xcos^{2}(\frac{1}{180}πx)}{16200sin^{3}(\frac{1}{180}πx)} + \frac{π^{2}x}{32400sin(\frac{1}{180}πx)}\\ \end{split}\end{equation} \]

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