There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ {{{{{x}^{sin(x)}}^{cos(x)}}^{tan(x)}}^{ln(x)}}^{e}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( {{{{{x}^{sin(x)}}^{cos(x)}}^{tan(x)}}^{ln(x)}}^{e}\right)}{dx}\\=&({{{{{x}^{sin(x)}}^{cos(x)}}^{tan(x)}}^{ln(x)}}^{e}((0)ln({{{{x}^{sin(x)}}^{cos(x)}}^{tan(x)}}^{ln(x)}) + \frac{(e)(({{{{x}^{sin(x)}}^{cos(x)}}^{tan(x)}}^{ln(x)}((\frac{1}{(x)})ln({{{x}^{sin(x)}}^{cos(x)}}^{tan(x)}) + \frac{(ln(x))(({{{x}^{sin(x)}}^{cos(x)}}^{tan(x)}((sec^{2}(x)(1))ln({{x}^{sin(x)}}^{cos(x)}) + \frac{(tan(x))(({{x}^{sin(x)}}^{cos(x)}((-sin(x))ln({x}^{sin(x)}) + \frac{(cos(x))(({x}^{sin(x)}((cos(x))ln(x) + \frac{(sin(x))(1)}{(x)})))}{({x}^{sin(x)})})))}{({{x}^{sin(x)}}^{cos(x)})})))}{({{{x}^{sin(x)}}^{cos(x)}}^{tan(x)})})))}{({{{{x}^{sin(x)}}^{cos(x)}}^{tan(x)}}^{ln(x)})}))\\=&\frac{{{{{{x}^{sin(x)}}^{cos(x)}}^{tan(x)}}^{ln(x)}}^{e}eln(x)sin(x)cos(x)tan(x)}{x} + {{{{{x}^{sin(x)}}^{cos(x)}}^{tan(x)}}^{ln(x)}}^{e}eln({{x}^{sin(x)}}^{cos(x)})ln(x)sec^{2}(x) - {{{{{x}^{sin(x)}}^{cos(x)}}^{tan(x)}}^{ln(x)}}^{e}eln({x}^{sin(x)})ln(x)sin(x)tan(x) + {{{{{x}^{sin(x)}}^{cos(x)}}^{tan(x)}}^{ln(x)}}^{e}eln^{2}(x)cos^{2}(x)tan(x) + \frac{{{{{{x}^{sin(x)}}^{cos(x)}}^{tan(x)}}^{ln(x)}}^{e}eln({{{x}^{sin(x)}}^{cos(x)}}^{tan(x)})}{x}\\ \end{split}\end{equation} \]

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