There are 1 questions in this calculation: for each question, the 4 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ {(x - 1)}^{\frac{1}{2}}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( (x - 1)^{\frac{1}{2}}\right)}{dx}\\=&((x - 1)^{\frac{1}{2}}((0)ln(x - 1) + \frac{(\frac{1}{2})(1 + 0)}{(x - 1)}))\\=&\frac{(x - 1)^{\frac{1}{2}}}{2(x - 1)}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{(x - 1)^{\frac{1}{2}}}{2(x - 1)}\right)}{dx}\\=&\frac{(\frac{\frac{1}{2}(1 + 0)}{(x - 1)^{\frac{1}{2}}})}{2(x - 1)} + \frac{(x - 1)^{\frac{1}{2}}(\frac{-(1 + 0)}{(x - 1)^{2}})}{2}\\=&\frac{-1}{4(x - 1)^{\frac{3}{2}}}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( \frac{-1}{4(x - 1)^{\frac{3}{2}}}\right)}{dx}\\=&\frac{-(\frac{\frac{-3}{2}(1 + 0)}{(x - 1)^{\frac{5}{2}}})}{4}\\=&\frac{3}{8(x - 1)^{\frac{5}{2}}}\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( \frac{3}{8(x - 1)^{\frac{5}{2}}}\right)}{dx}\\=&\frac{3(\frac{\frac{-5}{2}(1 + 0)}{(x - 1)^{\frac{7}{2}}})}{8}\\=&\frac{-15}{16(x - 1)^{\frac{7}{2}}}\\ \end{split}\end{equation} \]

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