There are 1 questions in this calculation: for each question, the 4 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ {{{{x}^{\frac{1}{2}}}^{\frac{1}{2}}}^{\frac{1}{2}}}^{\frac{1}{2}}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( {{{{x}^{\frac{1}{2}}}^{\frac{1}{2}}}^{\frac{1}{2}}}^{\frac{1}{2}}\right)}{dx}\\=&({{{{x}^{\frac{1}{2}}}^{\frac{1}{2}}}^{\frac{1}{2}}}^{\frac{1}{2}}((0)ln({{{x}^{\frac{1}{2}}}^{\frac{1}{2}}}^{\frac{1}{2}}) + \frac{(\frac{1}{2})(({{{x}^{\frac{1}{2}}}^{\frac{1}{2}}}^{\frac{1}{2}}((0)ln({{x}^{\frac{1}{2}}}^{\frac{1}{2}}) + \frac{(\frac{1}{2})(({{x}^{\frac{1}{2}}}^{\frac{1}{2}}((0)ln({x}^{\frac{1}{2}}) + \frac{(\frac{1}{2})(({x}^{\frac{1}{2}}((0)ln(x) + \frac{(\frac{1}{2})(1)}{(x)})))}{({x}^{\frac{1}{2}})})))}{({{x}^{\frac{1}{2}}}^{\frac{1}{2}})})))}{({{{x}^{\frac{1}{2}}}^{\frac{1}{2}}}^{\frac{1}{2}})}))\\=&\frac{1}{16x^{\frac{15}{16}}}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{1}{16x^{\frac{15}{16}}}\right)}{dx}\\=&\frac{\frac{-15}{16}}{16x^{\frac{31}{16}}}\\=&\frac{-15}{256x^{\frac{31}{16}}}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( \frac{-15}{256x^{\frac{31}{16}}}\right)}{dx}\\=&\frac{-15*\frac{-31}{16}}{256x^{\frac{47}{16}}}\\=&\frac{465}{4096x^{\frac{47}{16}}}\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( \frac{465}{4096x^{\frac{47}{16}}}\right)}{dx}\\=&\frac{465*\frac{-47}{16}}{4096x^{\frac{63}{16}}}\\=&\frac{-21855}{65536x^{\frac{63}{16}}}\\ \end{split}\end{equation} \]

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