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

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