求导函数：
输入一个原函数（即需要求导的函数），然后设置需要求导的变量和求导的阶数，点击“下一步”按钮，即可获得该函数相应阶数的导函数。
注意，输入的函数支持数学函数和其它常量。
输入一个原函数（即需要求导的函数），然后设置需要求导的变量和求导的阶数，点击“下一步”按钮，即可获得该函数相应阶数的导函数。
注意，输入的函数支持数学函数和其它常量。
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。
\[ \begin{equation}\begin{split}【1/1】求函数((1 - {a}^{2}){x}^{2} + 2a(1 - a)x + {a}^{2}{t}^{2})({\frac{1}{(x + a)}}^{2} + \frac{1}{({(a - 1)}^{2}x + a{t}^{2})}) 关于 x 的 1 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = \frac{x^{2}}{(x + a)^{2}} + \frac{x^{2}}{(a^{2}x - 2ax + x + at^{2})} - \frac{a^{2}x^{2}}{(x + a)^{2}} - \frac{a^{2}x^{2}}{(a^{2}x - 2ax + x + at^{2})} + \frac{2ax}{(x + a)^{2}} + \frac{2ax}{(a^{2}x - 2ax + x + at^{2})} - \frac{2a^{2}x}{(x + a)^{2}} - \frac{2a^{2}x}{(a^{2}x - 2ax + x + at^{2})} + \frac{a^{2}t^{2}}{(x + a)^{2}} + \frac{a^{2}t^{2}}{(a^{2}x - 2ax + x + at^{2})}\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( \frac{x^{2}}{(x + a)^{2}} + \frac{x^{2}}{(a^{2}x - 2ax + x + at^{2})} - \frac{a^{2}x^{2}}{(x + a)^{2}} - \frac{a^{2}x^{2}}{(a^{2}x - 2ax + x + at^{2})} + \frac{2ax}{(x + a)^{2}} + \frac{2ax}{(a^{2}x - 2ax + x + at^{2})} - \frac{2a^{2}x}{(x + a)^{2}} - \frac{2a^{2}x}{(a^{2}x - 2ax + x + at^{2})} + \frac{a^{2}t^{2}}{(x + a)^{2}} + \frac{a^{2}t^{2}}{(a^{2}x - 2ax + x + at^{2})}\right)}{dx}\\=&(\frac{-2(1 + 0)}{(x + a)^{3}})x^{2} + \frac{2x}{(x + a)^{2}} + (\frac{-(a^{2} - 2a + 1 + 0)}{(a^{2}x - 2ax + x + at^{2})^{2}})x^{2} + \frac{2x}{(a^{2}x - 2ax + x + at^{2})} - (\frac{-2(1 + 0)}{(x + a)^{3}})a^{2}x^{2} - \frac{a^{2}*2x}{(x + a)^{2}} - (\frac{-(a^{2} - 2a + 1 + 0)}{(a^{2}x - 2ax + x + at^{2})^{2}})a^{2}x^{2} - \frac{a^{2}*2x}{(a^{2}x - 2ax + x + at^{2})} + 2(\frac{-2(1 + 0)}{(x + a)^{3}})ax + \frac{2a}{(x + a)^{2}} + 2(\frac{-(a^{2} - 2a + 1 + 0)}{(a^{2}x - 2ax + x + at^{2})^{2}})ax + \frac{2a}{(a^{2}x - 2ax + x + at^{2})} - 2(\frac{-2(1 + 0)}{(x + a)^{3}})a^{2}x - \frac{2a^{2}}{(x + a)^{2}} - 2(\frac{-(a^{2} - 2a + 1 + 0)}{(a^{2}x - 2ax + x + at^{2})^{2}})a^{2}x - \frac{2a^{2}}{(a^{2}x - 2ax + x + at^{2})} + (\frac{-2(1 + 0)}{(x + a)^{3}})a^{2}t^{2} + 0 + (\frac{-(a^{2} - 2a + 1 + 0)}{(a^{2}x - 2ax + x + at^{2})^{2}})a^{2}t^{2} + 0\\=&\frac{-2x^{2}}{(x + a)^{3}} + \frac{2x}{(x + a)^{2}} + \frac{2ax^{2}}{(a^{2}x - 2ax + x + at^{2})^{2}} - \frac{x^{2}}{(a^{2}x - 2ax + x + at^{2})^{2}} + \frac{2x}{(a^{2}x - 2ax + x + at^{2})} + \frac{2a^{2}x^{2}}{(x + a)^{3}} - \frac{2a^{2}x}{(x + a)^{2}} + \frac{a^{4}x^{2}}{(a^{2}x - 2ax + x + at^{2})^{2}} - \frac{2a^{3}x^{2}}{(a^{2}x - 2ax + x + at^{2})^{2}} - \frac{2a^{2}x}{(a^{2}x - 2ax + x + at^{2})} - \frac{4ax}{(x + a)^{3}} - \frac{6a^{3}x}{(a^{2}x - 2ax + x + at^{2})^{2}} + \frac{6a^{2}x}{(a^{2}x - 2ax + x + at^{2})^{2}} - \frac{2ax}{(a^{2}x - 2ax + x + at^{2})^{2}} + \frac{4a^{2}x}{(x + a)^{3}} + \frac{2a^{4}x}{(a^{2}x - 2ax + x + at^{2})^{2}} - \frac{2a^{2}t^{2}}{(x + a)^{3}} - \frac{a^{4}t^{2}}{(a^{2}x - 2ax + x + at^{2})^{2}} + \frac{2a^{3}t^{2}}{(a^{2}x - 2ax + x + at^{2})^{2}} - \frac{a^{2}t^{2}}{(a^{2}x - 2ax + x + at^{2})^{2}} + \frac{2a}{(x + a)^{2}} - \frac{2a^{2}}{(x + a)^{2}} + \frac{2a}{(a^{2}x - 2ax + x + at^{2})} - \frac{2a^{2}}{(a^{2}x - 2ax + x + at^{2})}\\ \end{split}\end{equation} \]
注意，变量是区分大小写的。
\[ \begin{equation}\begin{split}【1/1】求函数((1 - {a}^{2}){x}^{2} + 2a(1 - a)x + {a}^{2}{t}^{2})({\frac{1}{(x + a)}}^{2} + \frac{1}{({(a - 1)}^{2}x + a{t}^{2})}) 关于 x 的 1 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = \frac{x^{2}}{(x + a)^{2}} + \frac{x^{2}}{(a^{2}x - 2ax + x + at^{2})} - \frac{a^{2}x^{2}}{(x + a)^{2}} - \frac{a^{2}x^{2}}{(a^{2}x - 2ax + x + at^{2})} + \frac{2ax}{(x + a)^{2}} + \frac{2ax}{(a^{2}x - 2ax + x + at^{2})} - \frac{2a^{2}x}{(x + a)^{2}} - \frac{2a^{2}x}{(a^{2}x - 2ax + x + at^{2})} + \frac{a^{2}t^{2}}{(x + a)^{2}} + \frac{a^{2}t^{2}}{(a^{2}x - 2ax + x + at^{2})}\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( \frac{x^{2}}{(x + a)^{2}} + \frac{x^{2}}{(a^{2}x - 2ax + x + at^{2})} - \frac{a^{2}x^{2}}{(x + a)^{2}} - \frac{a^{2}x^{2}}{(a^{2}x - 2ax + x + at^{2})} + \frac{2ax}{(x + a)^{2}} + \frac{2ax}{(a^{2}x - 2ax + x + at^{2})} - \frac{2a^{2}x}{(x + a)^{2}} - \frac{2a^{2}x}{(a^{2}x - 2ax + x + at^{2})} + \frac{a^{2}t^{2}}{(x + a)^{2}} + \frac{a^{2}t^{2}}{(a^{2}x - 2ax + x + at^{2})}\right)}{dx}\\=&(\frac{-2(1 + 0)}{(x + a)^{3}})x^{2} + \frac{2x}{(x + a)^{2}} + (\frac{-(a^{2} - 2a + 1 + 0)}{(a^{2}x - 2ax + x + at^{2})^{2}})x^{2} + \frac{2x}{(a^{2}x - 2ax + x + at^{2})} - (\frac{-2(1 + 0)}{(x + a)^{3}})a^{2}x^{2} - \frac{a^{2}*2x}{(x + a)^{2}} - (\frac{-(a^{2} - 2a + 1 + 0)}{(a^{2}x - 2ax + x + at^{2})^{2}})a^{2}x^{2} - \frac{a^{2}*2x}{(a^{2}x - 2ax + x + at^{2})} + 2(\frac{-2(1 + 0)}{(x + a)^{3}})ax + \frac{2a}{(x + a)^{2}} + 2(\frac{-(a^{2} - 2a + 1 + 0)}{(a^{2}x - 2ax + x + at^{2})^{2}})ax + \frac{2a}{(a^{2}x - 2ax + x + at^{2})} - 2(\frac{-2(1 + 0)}{(x + a)^{3}})a^{2}x - \frac{2a^{2}}{(x + a)^{2}} - 2(\frac{-(a^{2} - 2a + 1 + 0)}{(a^{2}x - 2ax + x + at^{2})^{2}})a^{2}x - \frac{2a^{2}}{(a^{2}x - 2ax + x + at^{2})} + (\frac{-2(1 + 0)}{(x + a)^{3}})a^{2}t^{2} + 0 + (\frac{-(a^{2} - 2a + 1 + 0)}{(a^{2}x - 2ax + x + at^{2})^{2}})a^{2}t^{2} + 0\\=&\frac{-2x^{2}}{(x + a)^{3}} + \frac{2x}{(x + a)^{2}} + \frac{2ax^{2}}{(a^{2}x - 2ax + x + at^{2})^{2}} - \frac{x^{2}}{(a^{2}x - 2ax + x + at^{2})^{2}} + \frac{2x}{(a^{2}x - 2ax + x + at^{2})} + \frac{2a^{2}x^{2}}{(x + a)^{3}} - \frac{2a^{2}x}{(x + a)^{2}} + \frac{a^{4}x^{2}}{(a^{2}x - 2ax + x + at^{2})^{2}} - \frac{2a^{3}x^{2}}{(a^{2}x - 2ax + x + at^{2})^{2}} - \frac{2a^{2}x}{(a^{2}x - 2ax + x + at^{2})} - \frac{4ax}{(x + a)^{3}} - \frac{6a^{3}x}{(a^{2}x - 2ax + x + at^{2})^{2}} + \frac{6a^{2}x}{(a^{2}x - 2ax + x + at^{2})^{2}} - \frac{2ax}{(a^{2}x - 2ax + x + at^{2})^{2}} + \frac{4a^{2}x}{(x + a)^{3}} + \frac{2a^{4}x}{(a^{2}x - 2ax + x + at^{2})^{2}} - \frac{2a^{2}t^{2}}{(x + a)^{3}} - \frac{a^{4}t^{2}}{(a^{2}x - 2ax + x + at^{2})^{2}} + \frac{2a^{3}t^{2}}{(a^{2}x - 2ax + x + at^{2})^{2}} - \frac{a^{2}t^{2}}{(a^{2}x - 2ax + x + at^{2})^{2}} + \frac{2a}{(x + a)^{2}} - \frac{2a^{2}}{(x + a)^{2}} + \frac{2a}{(a^{2}x - 2ax + x + at^{2})} - \frac{2a^{2}}{(a^{2}x - 2ax + x + at^{2})}\\ \end{split}\end{equation} \]
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