本次共计算 1 个题目：每一题对 y 求 1 阶导数。
    注意，变量是区分大小写的。
\[ \begin{equation}\begin{split}【1/1】求函数\frac{(1 - {e}^{(\frac{({x}^{2} - {y}^{2})}{4vt})})y}{({x}^{2} + {y}^{2})} 关于 y 的 1 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = - \frac{y{e}^{(\frac{\frac{1}{4}x^{2}}{vt} - \frac{\frac{1}{4}y^{2}}{vt})}}{(x^{2} + y^{2})} + \frac{y}{(x^{2} + y^{2})}\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( - \frac{y{e}^{(\frac{\frac{1}{4}x^{2}}{vt} - \frac{\frac{1}{4}y^{2}}{vt})}}{(x^{2} + y^{2})} + \frac{y}{(x^{2} + y^{2})}\right)}{dy}\\=& - (\frac{-(0 + 2y)}{(x^{2} + y^{2})^{2}})y{e}^{(\frac{\frac{1}{4}x^{2}}{vt} - \frac{\frac{1}{4}y^{2}}{vt})} - \frac{{e}^{(\frac{\frac{1}{4}x^{2}}{vt} - \frac{\frac{1}{4}y^{2}}{vt})}}{(x^{2} + y^{2})} - \frac{y({e}^{(\frac{\frac{1}{4}x^{2}}{vt} - \frac{\frac{1}{4}y^{2}}{vt})}((0 - \frac{\frac{1}{4}*2y}{vt})ln(e) + \frac{(\frac{\frac{1}{4}x^{2}}{vt} - \frac{\frac{1}{4}y^{2}}{vt})(0)}{(e)}))}{(x^{2} + y^{2})} + (\frac{-(0 + 2y)}{(x^{2} + y^{2})^{2}})y + \frac{1}{(x^{2} + y^{2})}\\=&\frac{2y^{2}{e}^{(\frac{\frac{1}{4}x^{2}}{vt} - \frac{\frac{1}{4}y^{2}}{vt})}}{(x^{2} + y^{2})^{2}} - \frac{{e}^{(\frac{\frac{1}{4}x^{2}}{vt} - \frac{\frac{1}{4}y^{2}}{vt})}}{(x^{2} + y^{2})} + \frac{y^{2}{e}^{(\frac{\frac{1}{4}x^{2}}{vt} - \frac{\frac{1}{4}y^{2}}{vt})}}{2(x^{2} + y^{2})vt} - \frac{2y^{2}}{(x^{2} + y^{2})^{2}} + \frac{1}{(x^{2} + y^{2})}\\ \end{split}\end{equation} \]

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