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。
\[ \begin{equation}\begin{split}【1/1】求函数({x}^{2} + 2{y}^{2} + 3{z}^{2}){e}^{(-({x}^{2} + {y}^{2} + {z}^{2}))} 关于 x 的 1 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = x^{2}{e}^{(-x^{2} - y^{2} - z^{2})} + 2y^{2}{e}^{(-x^{2} - y^{2} - z^{2})} + 3z^{2}{e}^{(-x^{2} - y^{2} - z^{2})}\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( x^{2}{e}^{(-x^{2} - y^{2} - z^{2})} + 2y^{2}{e}^{(-x^{2} - y^{2} - z^{2})} + 3z^{2}{e}^{(-x^{2} - y^{2} - z^{2})}\right)}{dx}\\=&2x{e}^{(-x^{2} - y^{2} - z^{2})} + x^{2}({e}^{(-x^{2} - y^{2} - z^{2})}((-2x + 0 + 0)ln(e) + \frac{(-x^{2} - y^{2} - z^{2})(0)}{(e)})) + 2y^{2}({e}^{(-x^{2} - y^{2} - z^{2})}((-2x + 0 + 0)ln(e) + \frac{(-x^{2} - y^{2} - z^{2})(0)}{(e)})) + 3z^{2}({e}^{(-x^{2} - y^{2} - z^{2})}((-2x + 0 + 0)ln(e) + \frac{(-x^{2} - y^{2} - z^{2})(0)}{(e)}))\\=&2x{e}^{(-x^{2} - y^{2} - z^{2})} - 2x^{3}{e}^{(-x^{2} - y^{2} - z^{2})} - 4y^{2}x{e}^{(-x^{2} - y^{2} - z^{2})} - 6z^{2}x{e}^{(-x^{2} - y^{2} - z^{2})}\\ \end{split}\end{equation} \]

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