There are 1 questions in this calculation: for each question, the 4 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ e^{e^{logx}}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( e^{e^{logx}}\right)}{dx}\\=&e^{e^{logx}}e^{logx}log\\=&loge^{e^{logx}}e^{logx}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( loge^{e^{logx}}e^{logx}\right)}{dx}\\=&loge^{e^{logx}}e^{logx}loge^{logx} + loge^{e^{logx}}e^{logx}log\\=&l^{2}o^{2}g^{2}e^{e^{logx}}e^{{logx}*{2}} + l^{2}o^{2}g^{2}e^{e^{logx}}e^{logx}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( l^{2}o^{2}g^{2}e^{e^{logx}}e^{{logx}*{2}} + l^{2}o^{2}g^{2}e^{e^{logx}}e^{logx}\right)}{dx}\\=&l^{2}o^{2}g^{2}e^{e^{logx}}e^{logx}loge^{{logx}*{2}} + l^{2}o^{2}g^{2}e^{e^{logx}}*2e^{logx}e^{logx}log + l^{2}o^{2}g^{2}e^{e^{logx}}e^{logx}loge^{logx} + l^{2}o^{2}g^{2}e^{e^{logx}}e^{logx}log\\=&l^{3}o^{3}g^{3}e^{e^{logx}}e^{{logx}*{3}} + 2l^{3}o^{3}g^{3}e^{{logx}*{2}}e^{e^{logx}} + l^{3}o^{3}g^{3}e^{e^{logx}}e^{{logx}*{2}} + l^{3}o^{3}g^{3}e^{e^{logx}}e^{logx}\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( l^{3}o^{3}g^{3}e^{e^{logx}}e^{{logx}*{3}} + 2l^{3}o^{3}g^{3}e^{{logx}*{2}}e^{e^{logx}} + l^{3}o^{3}g^{3}e^{e^{logx}}e^{{logx}*{2}} + l^{3}o^{3}g^{3}e^{e^{logx}}e^{logx}\right)}{dx}\\=&l^{3}o^{3}g^{3}e^{e^{logx}}e^{logx}loge^{{logx}*{3}} + l^{3}o^{3}g^{3}e^{e^{logx}}*3e^{{logx}*{2}}e^{logx}log + 2l^{3}o^{3}g^{3}*2e^{logx}e^{logx}loge^{e^{logx}} + 2l^{3}o^{3}g^{3}e^{{logx}*{2}}e^{e^{logx}}e^{logx}log + l^{3}o^{3}g^{3}e^{e^{logx}}e^{logx}loge^{{logx}*{2}} + l^{3}o^{3}g^{3}e^{e^{logx}}*2e^{logx}e^{logx}log + l^{3}o^{3}g^{3}e^{e^{logx}}e^{logx}loge^{logx} + l^{3}o^{3}g^{3}e^{e^{logx}}e^{logx}log\\=&l^{4}o^{4}g^{4}e^{e^{logx}}e^{{logx}*{4}} + 5l^{4}o^{4}g^{4}e^{{logx}*{3}}e^{e^{logx}} + 6l^{4}o^{4}g^{4}e^{{logx}*{2}}e^{e^{logx}} + l^{4}o^{4}g^{4}e^{e^{logx}}e^{{logx}*{3}} + l^{4}o^{4}g^{4}e^{e^{logx}}e^{{logx}*{2}} + l^{4}o^{4}g^{4}e^{e^{logx}}e^{logx}\\ \end{split}\end{equation} \]

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