本次共计算 1 个题目：每一题对 x 求 1 阶导数。
    注意，变量是区分大小写的。
\[ \begin{equation}\begin{split}【1/1】求函数e^{-({(x - X)}^{2})}e^{-({(y - Y)}^{2})}e^{cos(z)}e^{cos(arctan(\frac{y}{x}) - Z)} 关于 x 的 1 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = e^{-x^{2} + 2Xx - X^{2}}e^{2yY - y^{2} - Y^{2}}e^{cos(z)}e^{cos(arctan(\frac{y}{x}) - Z)}\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( e^{-x^{2} + 2Xx - X^{2}}e^{2yY - y^{2} - Y^{2}}e^{cos(z)}e^{cos(arctan(\frac{y}{x}) - Z)}\right)}{dx}\\=&e^{-x^{2} + 2Xx - X^{2}}(-2x + 2X + 0)e^{2yY - y^{2} - Y^{2}}e^{cos(z)}e^{cos(arctan(\frac{y}{x}) - Z)} + e^{-x^{2} + 2Xx - X^{2}}e^{2yY - y^{2} - Y^{2}}(0 + 0 + 0)e^{cos(z)}e^{cos(arctan(\frac{y}{x}) - Z)} + e^{-x^{2} + 2Xx - X^{2}}e^{2yY - y^{2} - Y^{2}}e^{cos(z)}*-sin(z)*0e^{cos(arctan(\frac{y}{x}) - Z)} + e^{-x^{2} + 2Xx - X^{2}}e^{2yY - y^{2} - Y^{2}}e^{cos(z)}e^{cos(arctan(\frac{y}{x}) - Z)}*-sin(arctan(\frac{y}{x}) - Z)((\frac{(\frac{y*-1}{x^{2}})}{(1 + (\frac{y}{x})^{2})}) + 0)\\=&-2xe^{-x^{2} + 2Xx - X^{2}}e^{2yY - y^{2} - Y^{2}}e^{cos(z)}e^{cos(arctan(\frac{y}{x}) - Z)} + 2Xe^{-x^{2} + 2Xx - X^{2}}e^{2yY - y^{2} - Y^{2}}e^{cos(z)}e^{cos(arctan(\frac{y}{x}) - Z)} + \frac{ye^{-x^{2} + 2Xx - X^{2}}e^{2yY - y^{2} - Y^{2}}e^{cos(z)}e^{cos(arctan(\frac{y}{x}) - Z)}sin(arctan(\frac{y}{x}) - Z)}{(\frac{y^{2}}{x^{2}} + 1)x^{2}}\\ \end{split}\end{equation} \]

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