There are 1 questions in this calculation: for each question, the 15 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 15th\ derivative\ of\ function\ \frac{x}{sin(x)}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ \\ &\color{blue}{The\ 15th\ derivative\ of\ function:} \\=&\frac{1307674368000cos^{14}(x)}{sin^{15}(x)} + \frac{5884534656000cos^{12}(x)}{sin^{13}(x)} + \frac{10733827104000cos^{10}(x)}{sin^{11}(x)} + \frac{10100314224000cos^{8}(x)}{sin^{9}(x)} + \frac{5136892160400cos^{6}(x)}{sin^{7}(x)} + \frac{1334495471400cos^{4}(x)}{sin^{5}(x)} + \frac{143941133730cos^{2}(x)}{sin^{3}(x)} + \frac{2990414715}{sin(x)} - \frac{1307674368000xcos^{15}(x)}{sin^{16}(x)} - \frac{6320426112000xcos^{13}(x)}{sin^{14}(x)} - \frac{12579100934400xcos^{11}(x)}{sin^{12}(x)} - \frac{13216073270400xcos^{9}(x)}{sin^{10}(x)} - \frac{7784050594320xcos^{7}(x)}{sin^{8}(x)} - \frac{2499588687960xcos^{5}(x)}{sin^{6}(x)} - \frac{384653685786xcos^{3}(x)}{sin^{4}(x)} - \frac{19391512145xcos(x)}{sin^{2}(x)}\\ \end{split}\end{equation} \]

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