There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ \frac{(1 - {e}^{(\frac{(-{x}^{2} - {y}^{2})}{4vt})})(-1)x}{({x}^{2} + {y}^{2})}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{x{e}^{(\frac{\frac{-1}{4}x^{2}}{vt} - \frac{\frac{1}{4}y^{2}}{vt})}}{(x^{2} + y^{2})} - \frac{x}{(x^{2} + y^{2})}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{x{e}^{(\frac{\frac{-1}{4}x^{2}}{vt} - \frac{\frac{1}{4}y^{2}}{vt})}}{(x^{2} + y^{2})} - \frac{x}{(x^{2} + y^{2})}\right)}{dx}\\=&(\frac{-(2x + 0)}{(x^{2} + y^{2})^{2}})x{e}^{(\frac{\frac{-1}{4}x^{2}}{vt} - \frac{\frac{1}{4}y^{2}}{vt})} + \frac{{e}^{(\frac{\frac{-1}{4}x^{2}}{vt} - \frac{\frac{1}{4}y^{2}}{vt})}}{(x^{2} + y^{2})} + \frac{x({e}^{(\frac{\frac{-1}{4}x^{2}}{vt} - \frac{\frac{1}{4}y^{2}}{vt})}((\frac{\frac{-1}{4}*2x}{vt} + 0)ln(e) + \frac{(\frac{\frac{-1}{4}x^{2}}{vt} - \frac{\frac{1}{4}y^{2}}{vt})(0)}{(e)}))}{(x^{2} + y^{2})} - (\frac{-(2x + 0)}{(x^{2} + y^{2})^{2}})x - \frac{1}{(x^{2} + y^{2})}\\=& - \frac{2x^{2}{e}^{(\frac{\frac{-1}{4}x^{2}}{vt} - \frac{\frac{1}{4}y^{2}}{vt})}}{(x^{2} + y^{2})^{2}} + \frac{{e}^{(\frac{\frac{-1}{4}x^{2}}{vt} - \frac{\frac{1}{4}y^{2}}{vt})}}{(x^{2} + y^{2})} - \frac{x^{2}{e}^{(\frac{\frac{-1}{4}x^{2}}{vt} - \frac{\frac{1}{4}y^{2}}{vt})}}{2(x^{2} + y^{2})vt} + \frac{2x^{2}}{(x^{2} + y^{2})^{2}} - \frac{1}{(x^{2} + y^{2})}\\ \end{split}\end{equation} \]

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