There are 1 questions in this calculation: for each question, the 4 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ e^{x - 1 - tan(x)}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = e^{x - tan(x) - 1}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( e^{x - tan(x) - 1}\right)}{dx}\\=&e^{x - tan(x) - 1}(1 - sec^{2}(x)(1) + 0)\\=& - e^{x - tan(x) - 1}sec^{2}(x) + e^{x - tan(x) - 1}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( - e^{x - tan(x) - 1}sec^{2}(x) + e^{x - tan(x) - 1}\right)}{dx}\\=& - e^{x - tan(x) - 1}(1 - sec^{2}(x)(1) + 0)sec^{2}(x) - e^{x - tan(x) - 1}*2sec^{2}(x)tan(x) + e^{x - tan(x) - 1}(1 - sec^{2}(x)(1) + 0)\\=& - 2e^{x - tan(x) - 1}sec^{2}(x) + e^{x - tan(x) - 1}sec^{4}(x) - 2e^{x - tan(x) - 1}tan(x)sec^{2}(x) + e^{x - tan(x) - 1}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( - 2e^{x - tan(x) - 1}sec^{2}(x) + e^{x - tan(x) - 1}sec^{4}(x) - 2e^{x - tan(x) - 1}tan(x)sec^{2}(x) + e^{x - tan(x) - 1}\right)}{dx}\\=& - 2e^{x - tan(x) - 1}(1 - sec^{2}(x)(1) + 0)sec^{2}(x) - 2e^{x - tan(x) - 1}*2sec^{2}(x)tan(x) + e^{x - tan(x) - 1}(1 - sec^{2}(x)(1) + 0)sec^{4}(x) + e^{x - tan(x) - 1}*4sec^{4}(x)tan(x) - 2e^{x - tan(x) - 1}(1 - sec^{2}(x)(1) + 0)tan(x)sec^{2}(x) - 2e^{x - tan(x) - 1}sec^{2}(x)(1)sec^{2}(x) - 2e^{x - tan(x) - 1}tan(x)*2sec^{2}(x)tan(x) + e^{x - tan(x) - 1}(1 - sec^{2}(x)(1) + 0)\\=&e^{x - tan(x) - 1}sec^{4}(x) + 6e^{x - tan(x) - 1}tan(x)sec^{4}(x) - e^{x - tan(x) - 1}sec^{6}(x) - 6e^{x - tan(x) - 1}tan(x)sec^{2}(x) - 3e^{x - tan(x) - 1}sec^{2}(x) - 4e^{x - tan(x) - 1}tan^{2}(x)sec^{2}(x) + e^{x - tan(x) - 1}\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( e^{x - tan(x) - 1}sec^{4}(x) + 6e^{x - tan(x) - 1}tan(x)sec^{4}(x) - e^{x - tan(x) - 1}sec^{6}(x) - 6e^{x - tan(x) - 1}tan(x)sec^{2}(x) - 3e^{x - tan(x) - 1}sec^{2}(x) - 4e^{x - tan(x) - 1}tan^{2}(x)sec^{2}(x) + e^{x - tan(x) - 1}\right)}{dx}\\=&e^{x - tan(x) - 1}(1 - sec^{2}(x)(1) + 0)sec^{4}(x) + e^{x - tan(x) - 1}*4sec^{4}(x)tan(x) + 6e^{x - tan(x) - 1}(1 - sec^{2}(x)(1) + 0)tan(x)sec^{4}(x) + 6e^{x - tan(x) - 1}sec^{2}(x)(1)sec^{4}(x) + 6e^{x - tan(x) - 1}tan(x)*4sec^{4}(x)tan(x) - e^{x - tan(x) - 1}(1 - sec^{2}(x)(1) + 0)sec^{6}(x) - e^{x - tan(x) - 1}*6sec^{6}(x)tan(x) - 6e^{x - tan(x) - 1}(1 - sec^{2}(x)(1) + 0)tan(x)sec^{2}(x) - 6e^{x - tan(x) - 1}sec^{2}(x)(1)sec^{2}(x) - 6e^{x - tan(x) - 1}tan(x)*2sec^{2}(x)tan(x) - 3e^{x - tan(x) - 1}(1 - sec^{2}(x)(1) + 0)sec^{2}(x) - 3e^{x - tan(x) - 1}*2sec^{2}(x)tan(x) - 4e^{x - tan(x) - 1}(1 - sec^{2}(x)(1) + 0)tan^{2}(x)sec^{2}(x) - 4e^{x - tan(x) - 1}*2tan(x)sec^{2}(x)(1)sec^{2}(x) - 4e^{x - tan(x) - 1}tan^{2}(x)*2sec^{2}(x)tan(x) + e^{x - tan(x) - 1}(1 - sec^{2}(x)(1) + 0)\\=&4e^{x - tan(x) - 1}sec^{6}(x) - 12e^{x - tan(x) - 1}tan(x)sec^{6}(x) + 8e^{x - tan(x) - 1}tan(x)sec^{4}(x) - 2e^{x - tan(x) - 1}sec^{4}(x) + 28e^{x - tan(x) - 1}tan^{2}(x)sec^{4}(x) + e^{x - tan(x) - 1}sec^{8}(x) - 12e^{x - tan(x) - 1}tan(x)sec^{2}(x) - 16e^{x - tan(x) - 1}tan^{2}(x)sec^{2}(x) - 4e^{x - tan(x) - 1}sec^{2}(x) - 8e^{x - tan(x) - 1}tan^{3}(x)sec^{2}(x) + e^{x - tan(x) - 1}\\ \end{split}\end{equation} \]

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