There are 1 questions in this calculation: for each question, the 4 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ th(e^{x})\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( th(e^{x})\right)}{dx}\\=&(1 - th^{2}(e^{x}))e^{x}\\=& - e^{x}th^{2}(e^{x}) + e^{x}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( - e^{x}th^{2}(e^{x}) + e^{x}\right)}{dx}\\=& - e^{x}th^{2}(e^{x}) - e^{x}*2th(e^{x})(1 - th^{2}(e^{x}))e^{x} + e^{x}\\=& - e^{x}th^{2}(e^{x}) - 2e^{{x}*{2}}th(e^{x}) + 2e^{{x}*{2}}th^{3}(e^{x}) + e^{x}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( - e^{x}th^{2}(e^{x}) - 2e^{{x}*{2}}th(e^{x}) + 2e^{{x}*{2}}th^{3}(e^{x}) + e^{x}\right)}{dx}\\=& - e^{x}th^{2}(e^{x}) - e^{x}*2th(e^{x})(1 - th^{2}(e^{x}))e^{x} - 2*2e^{x}e^{x}th(e^{x}) - 2e^{{x}*{2}}(1 - th^{2}(e^{x}))e^{x} + 2*2e^{x}e^{x}th^{3}(e^{x}) + 2e^{{x}*{2}}*3th^{2}(e^{x})(1 - th^{2}(e^{x}))e^{x} + e^{x}\\=& - e^{x}th^{2}(e^{x}) - 6e^{{x}*{2}}th(e^{x}) + 6e^{{x}*{2}}th^{3}(e^{x}) + 8e^{{x}*{3}}th^{2}(e^{x}) - 6e^{{x}*{3}}th^{4}(e^{x}) - 2e^{{x}*{3}} + e^{x}\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( - e^{x}th^{2}(e^{x}) - 6e^{{x}*{2}}th(e^{x}) + 6e^{{x}*{2}}th^{3}(e^{x}) + 8e^{{x}*{3}}th^{2}(e^{x}) - 6e^{{x}*{3}}th^{4}(e^{x}) - 2e^{{x}*{3}} + e^{x}\right)}{dx}\\=& - e^{x}th^{2}(e^{x}) - e^{x}*2th(e^{x})(1 - th^{2}(e^{x}))e^{x} - 6*2e^{x}e^{x}th(e^{x}) - 6e^{{x}*{2}}(1 - th^{2}(e^{x}))e^{x} + 6*2e^{x}e^{x}th^{3}(e^{x}) + 6e^{{x}*{2}}*3th^{2}(e^{x})(1 - th^{2}(e^{x}))e^{x} + 8*3e^{{x}*{2}}e^{x}th^{2}(e^{x}) + 8e^{{x}*{3}}*2th(e^{x})(1 - th^{2}(e^{x}))e^{x} - 6*3e^{{x}*{2}}e^{x}th^{4}(e^{x}) - 6e^{{x}*{3}}*4th^{3}(e^{x})(1 - th^{2}(e^{x}))e^{x} - 2*3e^{{x}*{2}}e^{x} + e^{x}\\=& - e^{x}th^{2}(e^{x}) - 14e^{{x}*{2}}th(e^{x}) + 14e^{{x}*{2}}th^{3}(e^{x}) + 48e^{{x}*{3}}th^{2}(e^{x}) - 36e^{{x}*{3}}th^{4}(e^{x}) + 16e^{{x}*{4}}th(e^{x}) - 40e^{{x}*{4}}th^{3}(e^{x}) + 24e^{{x}*{4}}th^{5}(e^{x}) - 12e^{{x}*{3}} + e^{x}\\ \end{split}\end{equation} \]

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