There are 1 questions in this calculation: for each question, the 4 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ e^{e^{xx}}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = e^{e^{x^{2}}}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( e^{e^{x^{2}}}\right)}{dx}\\=&e^{e^{x^{2}}}e^{x^{2}}*2x\\=&2xe^{x^{2}}e^{e^{x^{2}}}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( 2xe^{x^{2}}e^{e^{x^{2}}}\right)}{dx}\\=&2e^{x^{2}}e^{e^{x^{2}}} + 2xe^{x^{2}}*2xe^{e^{x^{2}}} + 2xe^{x^{2}}e^{e^{x^{2}}}e^{x^{2}}*2x\\=&2e^{x^{2}}e^{e^{x^{2}}} + 4x^{2}e^{x^{2}}e^{e^{x^{2}}} + 4x^{2}e^{e^{x^{2}}}e^{{x^{2}}*{2}}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( 2e^{x^{2}}e^{e^{x^{2}}} + 4x^{2}e^{x^{2}}e^{e^{x^{2}}} + 4x^{2}e^{e^{x^{2}}}e^{{x^{2}}*{2}}\right)}{dx}\\=&2e^{x^{2}}*2xe^{e^{x^{2}}} + 2e^{x^{2}}e^{e^{x^{2}}}e^{x^{2}}*2x + 4*2xe^{x^{2}}e^{e^{x^{2}}} + 4x^{2}e^{x^{2}}*2xe^{e^{x^{2}}} + 4x^{2}e^{x^{2}}e^{e^{x^{2}}}e^{x^{2}}*2x + 4*2xe^{e^{x^{2}}}e^{{x^{2}}*{2}} + 4x^{2}e^{e^{x^{2}}}e^{x^{2}}*2xe^{{x^{2}}*{2}} + 4x^{2}e^{e^{x^{2}}}*2e^{x^{2}}e^{x^{2}}*2x\\=&12xe^{x^{2}}e^{e^{x^{2}}} + 12xe^{e^{x^{2}}}e^{{x^{2}}*{2}} + 8x^{3}e^{x^{2}}e^{e^{x^{2}}} + 24x^{3}e^{e^{x^{2}}}e^{{x^{2}}*{2}} + 8x^{3}e^{{x^{2}}*{3}}e^{e^{x^{2}}}\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( 12xe^{x^{2}}e^{e^{x^{2}}} + 12xe^{e^{x^{2}}}e^{{x^{2}}*{2}} + 8x^{3}e^{x^{2}}e^{e^{x^{2}}} + 24x^{3}e^{e^{x^{2}}}e^{{x^{2}}*{2}} + 8x^{3}e^{{x^{2}}*{3}}e^{e^{x^{2}}}\right)}{dx}\\=&12e^{x^{2}}e^{e^{x^{2}}} + 12xe^{x^{2}}*2xe^{e^{x^{2}}} + 12xe^{x^{2}}e^{e^{x^{2}}}e^{x^{2}}*2x + 12e^{e^{x^{2}}}e^{{x^{2}}*{2}} + 12xe^{e^{x^{2}}}e^{x^{2}}*2xe^{{x^{2}}*{2}} + 12xe^{e^{x^{2}}}*2e^{x^{2}}e^{x^{2}}*2x + 8*3x^{2}e^{x^{2}}e^{e^{x^{2}}} + 8x^{3}e^{x^{2}}*2xe^{e^{x^{2}}} + 8x^{3}e^{x^{2}}e^{e^{x^{2}}}e^{x^{2}}*2x + 24*3x^{2}e^{e^{x^{2}}}e^{{x^{2}}*{2}} + 24x^{3}e^{e^{x^{2}}}e^{x^{2}}*2xe^{{x^{2}}*{2}} + 24x^{3}e^{e^{x^{2}}}*2e^{x^{2}}e^{x^{2}}*2x + 8*3x^{2}e^{{x^{2}}*{3}}e^{e^{x^{2}}} + 8x^{3}*3e^{{x^{2}}*{2}}e^{x^{2}}*2xe^{e^{x^{2}}} + 8x^{3}e^{{x^{2}}*{3}}e^{e^{x^{2}}}e^{x^{2}}*2x\\=&12e^{x^{2}}e^{e^{x^{2}}} + 48x^{2}e^{x^{2}}e^{e^{x^{2}}} + 144x^{2}e^{e^{x^{2}}}e^{{x^{2}}*{2}} + 12e^{e^{x^{2}}}e^{{x^{2}}*{2}} + 48x^{2}e^{{x^{2}}*{3}}e^{e^{x^{2}}} + 16x^{4}e^{x^{2}}e^{e^{x^{2}}} + 112x^{4}e^{e^{x^{2}}}e^{{x^{2}}*{2}} + 96x^{4}e^{{x^{2}}*{3}}e^{e^{x^{2}}} + 16x^{4}e^{e^{x^{2}}}e^{{x^{2}}*{4}}\\ \end{split}\end{equation} \]

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