There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ arctan({e}^{(sqrt(\frac{1}{3})(x - \frac{1}{2}t))})\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = arctan({e}^{(xsqrt(\frac{1}{3}) - \frac{1}{2}tsqrt(\frac{1}{3}))})\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( arctan({e}^{(xsqrt(\frac{1}{3}) - \frac{1}{2}tsqrt(\frac{1}{3}))})\right)}{dx}\\=&(\frac{(({e}^{(xsqrt(\frac{1}{3}) - \frac{1}{2}tsqrt(\frac{1}{3}))}((sqrt(\frac{1}{3}) + x*0*\frac{1}{2}*\frac{1}{3}^{\frac{1}{2}} - \frac{1}{2}t*0*\frac{1}{2}*\frac{1}{3}^{\frac{1}{2}})ln(e) + \frac{(xsqrt(\frac{1}{3}) - \frac{1}{2}tsqrt(\frac{1}{3}))(0)}{(e)})))}{(1 + ({e}^{(xsqrt(\frac{1}{3}) - \frac{1}{2}tsqrt(\frac{1}{3}))})^{2})})\\=&\frac{{e}^{(xsqrt(\frac{1}{3}) - \frac{1}{2}tsqrt(\frac{1}{3}))}sqrt(\frac{1}{3})}{({e}^{(2xsqrt(\frac{1}{3}) - tsqrt(\frac{1}{3}))} + 1)}\\ \end{split}\end{equation} \]

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