There are 1 questions in this calculation: for each question, the 4 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ e^{th(x)}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( e^{th(x)}\right)}{dx}\\=&e^{th(x)}(1 - th^{2}(x))\\=& - e^{th(x)}th^{2}(x) + e^{th(x)}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( - e^{th(x)}th^{2}(x) + e^{th(x)}\right)}{dx}\\=& - e^{th(x)}(1 - th^{2}(x))th^{2}(x) - e^{th(x)}*2th(x)(1 - th^{2}(x)) + e^{th(x)}(1 - th^{2}(x))\\=& - 2e^{th(x)}th^{2}(x) + e^{th(x)}th^{4}(x) - 2e^{th(x)}th(x) + 2e^{th(x)}th^{3}(x) + e^{th(x)}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( - 2e^{th(x)}th^{2}(x) + e^{th(x)}th^{4}(x) - 2e^{th(x)}th(x) + 2e^{th(x)}th^{3}(x) + e^{th(x)}\right)}{dx}\\=& - 2e^{th(x)}(1 - th^{2}(x))th^{2}(x) - 2e^{th(x)}*2th(x)(1 - th^{2}(x)) + e^{th(x)}(1 - th^{2}(x))th^{4}(x) + e^{th(x)}*4th^{3}(x)(1 - th^{2}(x)) - 2e^{th(x)}(1 - th^{2}(x))th(x) - 2e^{th(x)}(1 - th^{2}(x)) + 2e^{th(x)}(1 - th^{2}(x))th^{3}(x) + 2e^{th(x)}*3th^{2}(x)(1 - th^{2}(x)) + e^{th(x)}(1 - th^{2}(x))\\=&5e^{th(x)}th^{2}(x) - 3e^{th(x)}th^{4}(x) - e^{th(x)}th^{6}(x) + 12e^{th(x)}th^{3}(x) - 6e^{th(x)}th^{5}(x) - 6e^{th(x)}th(x) - e^{th(x)}\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( 5e^{th(x)}th^{2}(x) - 3e^{th(x)}th^{4}(x) - e^{th(x)}th^{6}(x) + 12e^{th(x)}th^{3}(x) - 6e^{th(x)}th^{5}(x) - 6e^{th(x)}th(x) - e^{th(x)}\right)}{dx}\\=&5e^{th(x)}(1 - th^{2}(x))th^{2}(x) + 5e^{th(x)}*2th(x)(1 - th^{2}(x)) - 3e^{th(x)}(1 - th^{2}(x))th^{4}(x) - 3e^{th(x)}*4th^{3}(x)(1 - th^{2}(x)) - e^{th(x)}(1 - th^{2}(x))th^{6}(x) - e^{th(x)}*6th^{5}(x)(1 - th^{2}(x)) + 12e^{th(x)}(1 - th^{2}(x))th^{3}(x) + 12e^{th(x)}*3th^{2}(x)(1 - th^{2}(x)) - 6e^{th(x)}(1 - th^{2}(x))th^{5}(x) - 6e^{th(x)}*5th^{4}(x)(1 - th^{2}(x)) - 6e^{th(x)}(1 - th^{2}(x))th(x) - 6e^{th(x)}(1 - th^{2}(x)) - e^{th(x)}(1 - th^{2}(x))\\=&48e^{th(x)}th^{2}(x) - 74e^{th(x)}th^{4}(x) + 32e^{th(x)}th^{6}(x) - 4e^{th(x)}th^{3}(x) + e^{th(x)}th^{8}(x) - 12e^{th(x)}th^{5}(x) + 12e^{th(x)}th^{7}(x) + 4e^{th(x)}th(x) - 7e^{th(x)}\\ \end{split}\end{equation} \]

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