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。
\[ \begin{equation}\begin{split}【1/1】求函数\frac{50(1 + x)}{((\frac{9}{2} - (1 + x)(1 + x)) - \frac{50(2 - x)}{((\frac{9}{2} - (2 - x)(1 + x)))})} 关于 x 的 1 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = \frac{50x}{(\frac{50x}{(x^{2} - x + \frac{5}{2})} - x^{2} - 2x - \frac{100}{(x^{2} - x + \frac{5}{2})} + \frac{7}{2})} + \frac{50}{(\frac{50x}{(x^{2} - x + \frac{5}{2})} - x^{2} - 2x - \frac{100}{(x^{2} - x + \frac{5}{2})} + \frac{7}{2})}\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( \frac{50x}{(\frac{50x}{(x^{2} - x + \frac{5}{2})} - x^{2} - 2x - \frac{100}{(x^{2} - x + \frac{5}{2})} + \frac{7}{2})} + \frac{50}{(\frac{50x}{(x^{2} - x + \frac{5}{2})} - x^{2} - 2x - \frac{100}{(x^{2} - x + \frac{5}{2})} + \frac{7}{2})}\right)}{dx}\\=&50(\frac{-(50(\frac{-(2x - 1 + 0)}{(x^{2} - x + \frac{5}{2})^{2}})x + \frac{50}{(x^{2} - x + \frac{5}{2})} - 2x - 2 - 100(\frac{-(2x - 1 + 0)}{(x^{2} - x + \frac{5}{2})^{2}}) + 0)}{(\frac{50x}{(x^{2} - x + \frac{5}{2})} - x^{2} - 2x - \frac{100}{(x^{2} - x + \frac{5}{2})} + \frac{7}{2})^{2}})x + \frac{50}{(\frac{50x}{(x^{2} - x + \frac{5}{2})} - x^{2} - 2x - \frac{100}{(x^{2} - x + \frac{5}{2})} + \frac{7}{2})} + 50(\frac{-(50(\frac{-(2x - 1 + 0)}{(x^{2} - x + \frac{5}{2})^{2}})x + \frac{50}{(x^{2} - x + \frac{5}{2})} - 2x - 2 - 100(\frac{-(2x - 1 + 0)}{(x^{2} - x + \frac{5}{2})^{2}}) + 0)}{(\frac{50x}{(x^{2} - x + \frac{5}{2})} - x^{2} - 2x - \frac{100}{(x^{2} - x + \frac{5}{2})} + \frac{7}{2})^{2}})\\=&\frac{5000x^{3}}{(\frac{50x}{(x^{2} - x + \frac{5}{2})} - x^{2} - 2x - \frac{100}{(x^{2} - x + \frac{5}{2})} + \frac{7}{2})^{2}(x^{2} - x + \frac{5}{2})^{2}} - \frac{7500x^{2}}{(\frac{50x}{(x^{2} - x + \frac{5}{2})} - x^{2} - 2x - \frac{100}{(x^{2} - x + \frac{5}{2})} + \frac{7}{2})^{2}(x^{2} - x + \frac{5}{2})^{2}} - \frac{2500x}{(\frac{50x}{(x^{2} - x + \frac{5}{2})} - x^{2} - 2x - \frac{100}{(x^{2} - x + \frac{5}{2})} + \frac{7}{2})^{2}(x^{2} - x + \frac{5}{2})} + \frac{100x^{2}}{(\frac{50x}{(x^{2} - x + \frac{5}{2})} - x^{2} - 2x - \frac{100}{(x^{2} - x + \frac{5}{2})} + \frac{7}{2})^{2}} + \frac{200x}{(\frac{50x}{(x^{2} - x + \frac{5}{2})} - x^{2} - 2x - \frac{100}{(x^{2} - x + \frac{5}{2})} + \frac{7}{2})^{2}} - \frac{7500x}{(\frac{50x}{(x^{2} - x + \frac{5}{2})} - x^{2} - 2x - \frac{100}{(x^{2} - x + \frac{5}{2})} + \frac{7}{2})^{2}(x^{2} - x + \frac{5}{2})^{2}} - \frac{2500}{(\frac{50x}{(x^{2} - x + \frac{5}{2})} - x^{2} - 2x - \frac{100}{(x^{2} - x + \frac{5}{2})} + \frac{7}{2})^{2}(x^{2} - x + \frac{5}{2})} + \frac{5000}{(\frac{50x}{(x^{2} - x + \frac{5}{2})} - x^{2} - 2x - \frac{100}{(x^{2} - x + \frac{5}{2})} + \frac{7}{2})^{2}(x^{2} - x + \frac{5}{2})^{2}} + \frac{50}{(\frac{50x}{(x^{2} - x + \frac{5}{2})} - x^{2} - 2x - \frac{100}{(x^{2} - x + \frac{5}{2})} + \frac{7}{2})} + \frac{100}{(\frac{50x}{(x^{2} - x + \frac{5}{2})} - x^{2} - 2x - \frac{100}{(x^{2} - x + \frac{5}{2})} + \frac{7}{2})^{2}}\\ \end{split}\end{equation} \]
注意，变量是区分大小写的。
\[ \begin{equation}\begin{split}【1/1】求函数\frac{50(1 + x)}{((\frac{9}{2} - (1 + x)(1 + x)) - \frac{50(2 - x)}{((\frac{9}{2} - (2 - x)(1 + x)))})} 关于 x 的 1 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = \frac{50x}{(\frac{50x}{(x^{2} - x + \frac{5}{2})} - x^{2} - 2x - \frac{100}{(x^{2} - x + \frac{5}{2})} + \frac{7}{2})} + \frac{50}{(\frac{50x}{(x^{2} - x + \frac{5}{2})} - x^{2} - 2x - \frac{100}{(x^{2} - x + \frac{5}{2})} + \frac{7}{2})}\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( \frac{50x}{(\frac{50x}{(x^{2} - x + \frac{5}{2})} - x^{2} - 2x - \frac{100}{(x^{2} - x + \frac{5}{2})} + \frac{7}{2})} + \frac{50}{(\frac{50x}{(x^{2} - x + \frac{5}{2})} - x^{2} - 2x - \frac{100}{(x^{2} - x + \frac{5}{2})} + \frac{7}{2})}\right)}{dx}\\=&50(\frac{-(50(\frac{-(2x - 1 + 0)}{(x^{2} - x + \frac{5}{2})^{2}})x + \frac{50}{(x^{2} - x + \frac{5}{2})} - 2x - 2 - 100(\frac{-(2x - 1 + 0)}{(x^{2} - x + \frac{5}{2})^{2}}) + 0)}{(\frac{50x}{(x^{2} - x + \frac{5}{2})} - x^{2} - 2x - \frac{100}{(x^{2} - x + \frac{5}{2})} + \frac{7}{2})^{2}})x + \frac{50}{(\frac{50x}{(x^{2} - x + \frac{5}{2})} - x^{2} - 2x - \frac{100}{(x^{2} - x + \frac{5}{2})} + \frac{7}{2})} + 50(\frac{-(50(\frac{-(2x - 1 + 0)}{(x^{2} - x + \frac{5}{2})^{2}})x + \frac{50}{(x^{2} - x + \frac{5}{2})} - 2x - 2 - 100(\frac{-(2x - 1 + 0)}{(x^{2} - x + \frac{5}{2})^{2}}) + 0)}{(\frac{50x}{(x^{2} - x + \frac{5}{2})} - x^{2} - 2x - \frac{100}{(x^{2} - x + \frac{5}{2})} + \frac{7}{2})^{2}})\\=&\frac{5000x^{3}}{(\frac{50x}{(x^{2} - x + \frac{5}{2})} - x^{2} - 2x - \frac{100}{(x^{2} - x + \frac{5}{2})} + \frac{7}{2})^{2}(x^{2} - x + \frac{5}{2})^{2}} - \frac{7500x^{2}}{(\frac{50x}{(x^{2} - x + \frac{5}{2})} - x^{2} - 2x - \frac{100}{(x^{2} - x + \frac{5}{2})} + \frac{7}{2})^{2}(x^{2} - x + \frac{5}{2})^{2}} - \frac{2500x}{(\frac{50x}{(x^{2} - x + \frac{5}{2})} - x^{2} - 2x - \frac{100}{(x^{2} - x + \frac{5}{2})} + \frac{7}{2})^{2}(x^{2} - x + \frac{5}{2})} + \frac{100x^{2}}{(\frac{50x}{(x^{2} - x + \frac{5}{2})} - x^{2} - 2x - \frac{100}{(x^{2} - x + \frac{5}{2})} + \frac{7}{2})^{2}} + \frac{200x}{(\frac{50x}{(x^{2} - x + \frac{5}{2})} - x^{2} - 2x - \frac{100}{(x^{2} - x + \frac{5}{2})} + \frac{7}{2})^{2}} - \frac{7500x}{(\frac{50x}{(x^{2} - x + \frac{5}{2})} - x^{2} - 2x - \frac{100}{(x^{2} - x + \frac{5}{2})} + \frac{7}{2})^{2}(x^{2} - x + \frac{5}{2})^{2}} - \frac{2500}{(\frac{50x}{(x^{2} - x + \frac{5}{2})} - x^{2} - 2x - \frac{100}{(x^{2} - x + \frac{5}{2})} + \frac{7}{2})^{2}(x^{2} - x + \frac{5}{2})} + \frac{5000}{(\frac{50x}{(x^{2} - x + \frac{5}{2})} - x^{2} - 2x - \frac{100}{(x^{2} - x + \frac{5}{2})} + \frac{7}{2})^{2}(x^{2} - x + \frac{5}{2})^{2}} + \frac{50}{(\frac{50x}{(x^{2} - x + \frac{5}{2})} - x^{2} - 2x - \frac{100}{(x^{2} - x + \frac{5}{2})} + \frac{7}{2})} + \frac{100}{(\frac{50x}{(x^{2} - x + \frac{5}{2})} - x^{2} - 2x - \frac{100}{(x^{2} - x + \frac{5}{2})} + \frac{7}{2})^{2}}\\ \end{split}\end{equation} \]
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