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

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