There are 1 questions in this calculation: for each question, the 4 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ sqrt(sqrt(x))\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( sqrt(sqrt(x))\right)}{dx}\\=&\frac{\frac{1}{2}*\frac{1}{2}}{(x)^{\frac{1}{2}}(sqrt(x))^{\frac{1}{2}}}\\=&\frac{1}{4x^{\frac{1}{2}}sqrt(x)^{\frac{1}{2}}}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{1}{4x^{\frac{1}{2}}sqrt(x)^{\frac{1}{2}}}\right)}{dx}\\=&\frac{\frac{-1}{2}}{4x^{\frac{3}{2}}sqrt(x)^{\frac{1}{2}}} + \frac{\frac{-1}{2}*\frac{1}{2}}{4x^{\frac{1}{2}}(x)^{\frac{3}{4}}(x)^{\frac{1}{2}}}\\=&\frac{-1}{8x^{\frac{3}{2}}sqrt(x)^{\frac{1}{2}}} - \frac{1}{16x^{\frac{7}{4}}}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( \frac{-1}{8x^{\frac{3}{2}}sqrt(x)^{\frac{1}{2}}} - \frac{1}{16x^{\frac{7}{4}}}\right)}{dx}\\=&\frac{-\frac{-3}{2}}{8x^{\frac{5}{2}}sqrt(x)^{\frac{1}{2}}} - \frac{\frac{-1}{2}*\frac{1}{2}}{8x^{\frac{3}{2}}(x)^{\frac{3}{4}}(x)^{\frac{1}{2}}} - \frac{\frac{-7}{4}}{16x^{\frac{11}{4}}}\\=&\frac{3}{16x^{\frac{5}{2}}sqrt(x)^{\frac{1}{2}}} + \frac{9}{64x^{\frac{11}{4}}}\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( \frac{3}{16x^{\frac{5}{2}}sqrt(x)^{\frac{1}{2}}} + \frac{9}{64x^{\frac{11}{4}}}\right)}{dx}\\=&\frac{3*\frac{-5}{2}}{16x^{\frac{7}{2}}sqrt(x)^{\frac{1}{2}}} + \frac{3*\frac{-1}{2}*\frac{1}{2}}{16x^{\frac{5}{2}}(x)^{\frac{3}{4}}(x)^{\frac{1}{2}}} + \frac{9*\frac{-11}{4}}{64x^{\frac{15}{4}}}\\=&\frac{-15}{32x^{\frac{7}{2}}sqrt(x)^{\frac{1}{2}}} - \frac{111}{256x^{\frac{15}{4}}}\\ \end{split}\end{equation} \]

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