There are 1 questions in this calculation: for each question, the 9 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 9th\ derivative\ of\ function\ {(1 + {(sin(x))}^{3})}^{\frac{1}{3}}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = (sin^{3}(x) + 1)^{\frac{1}{3}}\\\\ &\color{blue}{The\ 9th\ derivative\ of\ function:} \\=&\frac{96342400sin^{18}(x)cos^{9}(x)}{(sin^{3}(x) + 1)^{\frac{26}{3}}} - \frac{301593600sin^{15}(x)cos^{9}(x)}{(sin^{3}(x) + 1)^{\frac{23}{3}}} + \frac{150796800sin^{17}(x)cos^{7}(x)}{(sin^{3}(x) + 1)^{\frac{23}{3}}} + \frac{351859200sin^{12}(x)cos^{9}(x)}{(sin^{3}(x) + 1)^{\frac{20}{3}}} - \frac{439824000sin^{14}(x)cos^{7}(x)}{(sin^{3}(x) + 1)^{\frac{20}{3}}} + \frac{79168320sin^{16}(x)cos^{5}(x)}{(sin^{3}(x) + 1)^{\frac{20}{3}}} - \frac{186278400sin^{9}(x)cos^{9}(x)}{(sin^{3}(x) + 1)^{\frac{17}{3}}} + \frac{465696000sin^{11}(x)cos^{7}(x)}{(sin^{3}(x) + 1)^{\frac{17}{3}}} - \frac{212667840sin^{13}(x)cos^{5}(x)}{(sin^{3}(x) + 1)^{\frac{17}{3}}} + \frac{15523200sin^{15}(x)cos^{3}(x)}{(sin^{3}(x) + 1)^{\frac{17}{3}}} + \frac{42873600sin^{6}(x)cos^{9}(x)}{(sin^{3}(x) + 1)^{\frac{14}{3}}} - \frac{213628800sin^{8}(x)cos^{7}(x)}{(sin^{3}(x) + 1)^{\frac{14}{3}}} + \frac{200434080sin^{10}(x)cos^{5}(x)}{(sin^{3}(x) + 1)^{\frac{14}{3}}} - \frac{37699200sin^{12}(x)cos^{3}(x)}{(sin^{3}(x) + 1)^{\frac{14}{3}}} + \frac{831600sin^{14}(x)cos(x)}{(sin^{3}(x) + 1)^{\frac{14}{3}}} - \frac{3225600sin^{3}(x)cos^{9}(x)}{(sin^{3}(x) + 1)^{\frac{11}{3}}} + \frac{38707200sin^{5}(x)cos^{7}(x)}{(sin^{3}(x) + 1)^{\frac{11}{3}}} - \frac{76742400sin^{7}(x)cos^{5}(x)}{(sin^{3}(x) + 1)^{\frac{11}{3}}} + \frac{30609600sin^{9}(x)cos^{3}(x)}{(sin^{3}(x) + 1)^{\frac{11}{3}}} - \frac{1764000sin^{11}(x)cos(x)}{(sin^{3}(x) + 1)^{\frac{11}{3}}} - \frac{1747200sin^{2}(x)cos^{7}(x)}{(sin^{3}(x) + 1)^{\frac{8}{3}}} + \frac{9996000sin^{4}(x)cos^{5}(x)}{(sin^{3}(x) + 1)^{\frac{8}{3}}} + \frac{22400cos^{9}(x)}{(sin^{3}(x) + 1)^{\frac{8}{3}}} - \frac{9130600sin^{6}(x)cos^{3}(x)}{(sin^{3}(x) + 1)^{\frac{8}{3}}} + \frac{1156050sin^{8}(x)cos(x)}{(sin^{3}(x) + 1)^{\frac{8}{3}}} - \frac{188160sin(x)cos^{5}(x)}{(sin^{3}(x) + 1)^{\frac{5}{3}}} + \frac{698640sin^{3}(x)cos^{3}(x)}{(sin^{3}(x) + 1)^{\frac{5}{3}}} - \frac{228570sin^{5}(x)cos(x)}{(sin^{3}(x) + 1)^{\frac{5}{3}}} - \frac{1640cos^{3}(x)}{(sin^{3}(x) + 1)^{\frac{2}{3}}} + \frac{4921sin^{2}(x)cos(x)}{(sin^{3}(x) + 1)^{\frac{2}{3}}}\\ \end{split}\end{equation} \]

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