There are 1 questions in this calculation: for each question, the 9 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 9th\ derivative\ of\ function\ {x}^{(sin(2)x)}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = {x}^{(xsin(2))}\\\\ &\color{blue}{The\ 9th\ derivative\ of\ function:} \\=&{x}^{(xsin(2))}ln^{9}(x)sin^{9}(2) + 9{x}^{(xsin(2))}ln^{8}(x)sin^{9}(2) + \frac{36{x}^{(xsin(2))}ln^{7}(x)sin^{8}(2)}{x} + 36{x}^{(xsin(2))}ln^{7}(x)sin^{9}(2) + \frac{252{x}^{(xsin(2))}ln^{6}(x)sin^{8}(2)}{x} - \frac{84{x}^{(xsin(2))}ln^{6}(x)sin^{7}(2)}{x^{2}} + 84{x}^{(xsin(2))}ln^{6}(x)sin^{9}(2) + \frac{756{x}^{(xsin(2))}ln^{5}(x)sin^{8}(2)}{x} + \frac{630{x}^{(xsin(2))}ln^{4}(x)sin^{7}(2)}{x^{2}} + \frac{252{x}^{(xsin(2))}ln^{5}(x)sin^{6}(2)}{x^{3}} - \frac{126{x}^{(xsin(2))}ln^{5}(x)sin^{7}(2)}{x^{2}} + 126{x}^{(xsin(2))}ln^{5}(x)sin^{9}(2) + \frac{1260{x}^{(xsin(2))}ln^{4}(x)sin^{8}(2)}{x} + \frac{2100{x}^{(xsin(2))}ln^{3}(x)sin^{7}(2)}{x^{2}} - \frac{1260{x}^{(xsin(2))}ln^{3}(x)sin^{6}(2)}{x^{3}} - \frac{1260{x}^{(xsin(2))}ln^{2}(x)sin^{6}(2)}{x^{3}} - \frac{756{x}^{(xsin(2))}ln^{4}(x)sin^{5}(2)}{x^{4}} + \frac{336{x}^{(xsin(2))}ln^{3}(x)sin^{5}(2)}{x^{4}} + 126{x}^{(xsin(2))}ln^{4}(x)sin^{9}(2) + \frac{1260{x}^{(xsin(2))}ln^{3}(x)sin^{8}(2)}{x} + \frac{2520{x}^{(xsin(2))}ln^{2}(x)sin^{7}(2)}{x^{2}} + \frac{1764{x}^{(xsin(2))}ln^{2}(x)sin^{5}(2)}{x^{4}} - \frac{231{x}^{(xsin(2))}sin^{5}(2)}{x^{4}} + \frac{2016{x}^{(xsin(2))}ln^{3}(x)sin^{4}(2)}{x^{5}} - \frac{1008{x}^{(xsin(2))}ln^{2}(x)sin^{4}(2)}{x^{5}} - \frac{1764{x}^{(xsin(2))}ln(x)sin^{4}(2)}{x^{5}} + 84{x}^{(xsin(2))}ln^{3}(x)sin^{9}(2) + \frac{756{x}^{(xsin(2))}ln^{2}(x)sin^{8}(2)}{x} + \frac{1386{x}^{(xsin(2))}ln(x)sin^{7}(2)}{x^{2}} + \frac{252{x}^{(xsin(2))}sin^{6}(2)}{x^{3}} + \frac{441{x}^{(xsin(2))}ln(x)sin^{5}(2)}{x^{4}} - \frac{4320{x}^{(xsin(2))}ln^{2}(x)sin^{3}(2)}{x^{6}} + \frac{1692{x}^{(xsin(2))}ln(x)sin^{3}(2)}{x^{6}} + \frac{944{x}^{(xsin(2))}sin^{3}(2)}{x^{6}} + 36{x}^{(xsin(2))}ln^{2}(x)sin^{9}(2) + \frac{252{x}^{(xsin(2))}ln(x)sin^{8}(2)}{x} + \frac{294{x}^{(xsin(2))}sin^{7}(2)}{x^{2}} + \frac{6480{x}^{(xsin(2))}ln(x)sin^{2}(2)}{x^{7}} - \frac{1368{x}^{(xsin(2))}sin^{2}(2)}{x^{7}} + 9{x}^{(xsin(2))}ln(x)sin^{9}(2) + \frac{36{x}^{(xsin(2))}sin^{8}(2)}{x} - \frac{5040{x}^{(xsin(2))}sin(2)}{x^{8}} + {x}^{(xsin(2))}sin^{9}(2)\\ \end{split}\end{equation} \]

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