There are 1 questions in this calculation: for each question, the 4 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ x{\frac{1}{(x + 1)}}^{\frac{1}{3}}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( x{\frac{1}{(x + 1)}}^{\frac{1}{3}}\right)}{dx}\\=&{\frac{1}{(x + 1)}}^{\frac{1}{3}} + x({\frac{1}{(x + 1)}}^{\frac{1}{3}}((0)ln(\frac{1}{(x + 1)}) + \frac{(\frac{1}{3})((\frac{-(1 + 0)}{(x + 1)^{2}}))}{(\frac{1}{(x + 1)})}))\\=&\frac{-x}{3(x + 1)^{\frac{4}{3}}} + \frac{1}{(x + 1)^{\frac{1}{3}}}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{-x}{3(x + 1)^{\frac{4}{3}}} + \frac{1}{(x + 1)^{\frac{1}{3}}}\right)}{dx}\\=&\frac{-(\frac{\frac{-4}{3}(1 + 0)}{(x + 1)^{\frac{7}{3}}})x}{3} - \frac{1}{3(x + 1)^{\frac{4}{3}}} + (\frac{\frac{-1}{3}(1 + 0)}{(x + 1)^{\frac{4}{3}}})\\=&\frac{4x}{9(x + 1)^{\frac{7}{3}}} - \frac{2}{3(x + 1)^{\frac{4}{3}}}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( \frac{4x}{9(x + 1)^{\frac{7}{3}}} - \frac{2}{3(x + 1)^{\frac{4}{3}}}\right)}{dx}\\=&\frac{4(\frac{\frac{-7}{3}(1 + 0)}{(x + 1)^{\frac{10}{3}}})x}{9} + \frac{4}{9(x + 1)^{\frac{7}{3}}} - \frac{2(\frac{\frac{-4}{3}(1 + 0)}{(x + 1)^{\frac{7}{3}}})}{3}\\=&\frac{-28x}{27(x + 1)^{\frac{10}{3}}} + \frac{4}{3(x + 1)^{\frac{7}{3}}}\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( \frac{-28x}{27(x + 1)^{\frac{10}{3}}} + \frac{4}{3(x + 1)^{\frac{7}{3}}}\right)}{dx}\\=&\frac{-28(\frac{\frac{-10}{3}(1 + 0)}{(x + 1)^{\frac{13}{3}}})x}{27} - \frac{28}{27(x + 1)^{\frac{10}{3}}} + \frac{4(\frac{\frac{-7}{3}(1 + 0)}{(x + 1)^{\frac{10}{3}}})}{3}\\=&\frac{280x}{81(x + 1)^{\frac{13}{3}}} - \frac{112}{27(x + 1)^{\frac{10}{3}}}\\ \end{split}\end{equation} \]

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