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

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