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

你的问题在这里没有得到解决？请到 热门难题 里面看看吧！