There are 1 questions in this calculation: for each question, the 4 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ {sin(x)}^{(\frac{7}{3})}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( {sin(x)}^{\frac{7}{3}}\right)}{dx}\\=&({sin(x)}^{\frac{7}{3}}((0)ln(sin(x)) + \frac{(\frac{7}{3})(cos(x))}{(sin(x))}))\\=&\frac{7sin^{\frac{4}{3}}(x)cos(x)}{3}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{7sin^{\frac{4}{3}}(x)cos(x)}{3}\right)}{dx}\\=&\frac{7*\frac{4}{3}sin^{\frac{1}{3}}(x)cos(x)cos(x)}{3} + \frac{7sin^{\frac{4}{3}}(x)*-sin(x)}{3}\\=&\frac{28sin^{\frac{1}{3}}(x)cos^{2}(x)}{9} - \frac{7sin^{\frac{7}{3}}(x)}{3}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( \frac{28sin^{\frac{1}{3}}(x)cos^{2}(x)}{9} - \frac{7sin^{\frac{7}{3}}(x)}{3}\right)}{dx}\\=&\frac{28*\frac{1}{3}cos(x)cos^{2}(x)}{9sin^{\frac{2}{3}}(x)} + \frac{28sin^{\frac{1}{3}}(x)*-2cos(x)sin(x)}{9} - \frac{7*\frac{7}{3}sin^{\frac{4}{3}}(x)cos(x)}{3}\\=&\frac{28cos^{3}(x)}{27sin^{\frac{2}{3}}(x)} - \frac{35sin^{\frac{4}{3}}(x)cos(x)}{3}\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( \frac{28cos^{3}(x)}{27sin^{\frac{2}{3}}(x)} - \frac{35sin^{\frac{4}{3}}(x)cos(x)}{3}\right)}{dx}\\=&\frac{28*\frac{-2}{3}cos(x)cos^{3}(x)}{27sin^{\frac{5}{3}}(x)} + \frac{28*-3cos^{2}(x)sin(x)}{27sin^{\frac{2}{3}}(x)} - \frac{35*\frac{4}{3}sin^{\frac{1}{3}}(x)cos(x)cos(x)}{3} - \frac{35sin^{\frac{4}{3}}(x)*-sin(x)}{3}\\=&\frac{-56cos^{4}(x)}{81sin^{\frac{5}{3}}(x)} - \frac{56sin^{\frac{1}{3}}(x)cos^{2}(x)}{3} + \frac{35sin^{\frac{7}{3}}(x)}{3}\\ \end{split}\end{equation} \]

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