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

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