There are 1 questions in this calculation: for each question, the 9 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 9th\ derivative\ of\ function\ {(1 + sin(x))}^{\frac{1}{3}}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = (sin(x) + 1)^{\frac{1}{3}}\\\\ &\color{blue}{The\ 9th\ derivative\ of\ function:} \\=&\frac{96342400cos^{9}(x)}{19683(sin(x) + 1)^{\frac{26}{3}}} + \frac{123200sin(x)cos^{3}(x)}{27(sin(x) + 1)^{\frac{11}{3}}} - \frac{8200cos^{3}(x)}{27(sin(x) + 1)^{\frac{8}{3}}} + \frac{2450sin^{2}(x)cos(x)}{3(sin(x) + 1)^{\frac{8}{3}}} - \frac{1897280sin(x)cos^{5}(x)}{81(sin(x) + 1)^{\frac{17}{3}}} + \frac{283360cos^{5}(x)}{81(sin(x) + 1)^{\frac{14}{3}}} - \frac{492800sin^{2}(x)cos^{3}(x)}{27(sin(x) + 1)^{\frac{14}{3}}} - \frac{28000sin^{3}(x)cos(x)}{9(sin(x) + 1)^{\frac{11}{3}}} + \frac{2932160sin^{2}(x)cos^{5}(x)}{81(sin(x) + 1)^{\frac{20}{3}}} + \frac{1724800sin^{3}(x)cos^{3}(x)}{81(sin(x) + 1)^{\frac{17}{3}}} + \frac{16755200sin(x)cos^{7}(x)}{729(sin(x) + 1)^{\frac{23}{3}}} - \frac{5864320cos^{7}(x)}{729(sin(x) + 1)^{\frac{20}{3}}} + \frac{30800sin^{4}(x)cos(x)}{9(sin(x) + 1)^{\frac{14}{3}}} - \frac{170sin(x)cos(x)}{3(sin(x) + 1)^{\frac{5}{3}}} + \frac{cos(x)}{3(sin(x) + 1)^{\frac{2}{3}}}\\ \end{split}\end{equation} \]

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