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

你的问题在这里没有得到解决？请到 热门难题 里面看看吧！