数学
         
语言:中文    Language:English
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。
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    本次共计算 1 个题目:每一题对 x 求 2 阶导数。
    注意,变量是区分大小写的。
\[ \begin{equation}\begin{split}【1/1】求函数x{(\frac{(x - 1)(x - 2)}{((x - 3)(x - 4))})}^{\frac{1}{2}} 关于 x 的 2 阶导数:\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = (\frac{x^{2}}{(x - 3)(x - 4)} - \frac{3x}{(x - 3)(x - 4)} + \frac{2}{(x - 3)(x - 4)})^{\frac{1}{2}}x\\&\color{blue}{函数的第 1 阶导数:}\\&\frac{d\left( (\frac{x^{2}}{(x - 3)(x - 4)} - \frac{3x}{(x - 3)(x - 4)} + \frac{2}{(x - 3)(x - 4)})^{\frac{1}{2}}x\right)}{dx}\\=&(\frac{\frac{1}{2}(\frac{(\frac{-(1 + 0)}{(x - 3)^{2}})x^{2}}{(x - 4)} + \frac{(\frac{-(1 + 0)}{(x - 4)^{2}})x^{2}}{(x - 3)} + \frac{2x}{(x - 3)(x - 4)} - \frac{3(\frac{-(1 + 0)}{(x - 3)^{2}})x}{(x - 4)} - \frac{3(\frac{-(1 + 0)}{(x - 4)^{2}})x}{(x - 3)} - \frac{3}{(x - 3)(x - 4)} + \frac{2(\frac{-(1 + 0)}{(x - 3)^{2}})}{(x - 4)} + \frac{2(\frac{-(1 + 0)}{(x - 4)^{2}})}{(x - 3)})}{(\frac{x^{2}}{(x - 3)(x - 4)} - \frac{3x}{(x - 3)(x - 4)} + \frac{2}{(x - 3)(x - 4)})^{\frac{1}{2}}})x + (\frac{x^{2}}{(x - 3)(x - 4)} - \frac{3x}{(x - 3)(x - 4)} + \frac{2}{(x - 3)(x - 4)})^{\frac{1}{2}}\\=&\frac{-x^{3}}{2(\frac{x^{2}}{(x - 3)(x - 4)} - \frac{3x}{(x - 3)(x - 4)} + \frac{2}{(x - 3)(x - 4)})^{\frac{1}{2}}(x - 3)^{2}(x - 4)} - \frac{x^{3}}{2(\frac{x^{2}}{(x - 3)(x - 4)} - \frac{3x}{(x - 3)(x - 4)} + \frac{2}{(x - 3)(x - 4)})^{\frac{1}{2}}(x - 4)^{2}(x - 3)} + \frac{x^{2}}{(\frac{x^{2}}{(x - 3)(x - 4)} - \frac{3x}{(x - 3)(x - 4)} + \frac{2}{(x - 3)(x - 4)})^{\frac{1}{2}}(x - 4)(x - 3)} + \frac{3x^{2}}{2(\frac{x^{2}}{(x - 3)(x - 4)} - \frac{3x}{(x - 3)(x - 4)} + \frac{2}{(x - 3)(x - 4)})^{\frac{1}{2}}(x - 3)^{2}(x - 4)} + \frac{3x^{2}}{2(\frac{x^{2}}{(x - 3)(x - 4)} - \frac{3x}{(x - 3)(x - 4)} + \frac{2}{(x - 3)(x - 4)})^{\frac{1}{2}}(x - 4)^{2}(x - 3)} - \frac{3x}{2(\frac{x^{2}}{(x - 3)(x - 4)} - \frac{3x}{(x - 3)(x - 4)} + \frac{2}{(x - 3)(x - 4)})^{\frac{1}{2}}(x - 3)(x - 4)} - \frac{x}{(\frac{x^{2}}{(x - 3)(x - 4)} - \frac{3x}{(x - 3)(x - 4)} + \frac{2}{(x - 3)(x - 4)})^{\frac{1}{2}}(x - 3)^{2}(x - 4)} - \frac{x}{(\frac{x^{2}}{(x - 3)(x - 4)} - \frac{3x}{(x - 3)(x - 4)} + \frac{2}{(x - 3)(x - 4)})^{\frac{1}{2}}(x - 4)^{2}(x - 3)} + (\frac{x^{2}}{(x - 3)(x - 4)} - \frac{3x}{(x - 3)(x - 4)} + \frac{2}{(x - 3)(x - 4)})^{\frac{1}{2}}\\\\ &\color{blue}{函数的第 2 阶导数:} \\&\frac{d\left( \frac{-x^{3}}{2(\frac{x^{2}}{(x - 3)(x - 4)} - \frac{3x}{(x - 3)(x - 4)} + \frac{2}{(x - 3)(x - 4)})^{\frac{1}{2}}(x - 3)^{2}(x - 4)} - \frac{x^{3}}{2(\frac{x^{2}}{(x - 3)(x - 4)} - \frac{3x}{(x - 3)(x - 4)} + \frac{2}{(x - 3)(x - 4)})^{\frac{1}{2}}(x - 4)^{2}(x - 3)} + \frac{x^{2}}{(\frac{x^{2}}{(x - 3)(x - 4)} - \frac{3x}{(x - 3)(x - 4)} + \frac{2}{(x - 3)(x - 4)})^{\frac{1}{2}}(x - 4)(x - 3)} + \frac{3x^{2}}{2(\frac{x^{2}}{(x - 3)(x - 4)} - \frac{3x}{(x - 3)(x - 4)} + \frac{2}{(x - 3)(x - 4)})^{\frac{1}{2}}(x - 3)^{2}(x - 4)} + \frac{3x^{2}}{2(\frac{x^{2}}{(x - 3)(x - 4)} - \frac{3x}{(x - 3)(x - 4)} + \frac{2}{(x - 3)(x - 4)})^{\frac{1}{2}}(x - 4)^{2}(x - 3)} - \frac{3x}{2(\frac{x^{2}}{(x - 3)(x - 4)} - \frac{3x}{(x - 3)(x - 4)} + \frac{2}{(x - 3)(x - 4)})^{\frac{1}{2}}(x - 3)(x - 4)} - \frac{x}{(\frac{x^{2}}{(x - 3)(x - 4)} - \frac{3x}{(x - 3)(x - 4)} + \frac{2}{(x - 3)(x - 4)})^{\frac{1}{2}}(x - 3)^{2}(x - 4)} - \frac{x}{(\frac{x^{2}}{(x - 3)(x - 4)} - \frac{3x}{(x - 3)(x - 4)} + \frac{2}{(x - 3)(x - 4)})^{\frac{1}{2}}(x - 4)^{2}(x - 3)} + (\frac{x^{2}}{(x - 3)(x - 4)} - \frac{3x}{(x - 3)(x - 4)} + \frac{2}{(x - 3)(x - 4)})^{\frac{1}{2}}\right)}{dx}\\=&\frac{-(\frac{\frac{-1}{2}(\frac{(\frac{-(1 + 0)}{(x - 3)^{2}})x^{2}}{(x - 4)} + \frac{(\frac{-(1 + 0)}{(x - 4)^{2}})x^{2}}{(x - 3)} + \frac{2x}{(x - 3)(x - 4)} - \frac{3(\frac{-(1 + 0)}{(x - 3)^{2}})x}{(x - 4)} - \frac{3(\frac{-(1 + 0)}{(x - 4)^{2}})x}{(x - 3)} - \frac{3}{(x - 3)(x - 4)} + \frac{2(\frac{-(1 + 0)}{(x - 3)^{2}})}{(x - 4)} + \frac{2(\frac{-(1 + 0)}{(x - 4)^{2}})}{(x - 3)})}{(\frac{x^{2}}{(x - 3)(x - 4)} - \frac{3x}{(x - 3)(x - 4)} + \frac{2}{(x - 3)(x - 4)})^{\frac{3}{2}}})x^{3}}{2(x - 3)^{2}(x - 4)} - \frac{(\frac{-2(1 + 0)}{(x - 3)^{3}})x^{3}}{2(\frac{x^{2}}{(x - 3)(x - 4)} - \frac{3x}{(x - 3)(x - 4)} + \frac{2}{(x - 3)(x - 4)})^{\frac{1}{2}}(x - 4)} - \frac{(\frac{-(1 + 0)}{(x - 4)^{2}})x^{3}}{2(\frac{x^{2}}{(x - 3)(x - 4)} - \frac{3x}{(x - 3)(x - 4)} + \frac{2}{(x - 3)(x - 4)})^{\frac{1}{2}}(x - 3)^{2}} - \frac{3x^{2}}{2(\frac{x^{2}}{(x - 3)(x - 4)} - \frac{3x}{(x - 3)(x - 4)} + \frac{2}{(x - 3)(x - 4)})^{\frac{1}{2}}(x - 3)^{2}(x - 4)} - \frac{(\frac{\frac{-1}{2}(\frac{(\frac{-(1 + 0)}{(x - 3)^{2}})x^{2}}{(x - 4)} + \frac{(\frac{-(1 + 0)}{(x - 4)^{2}})x^{2}}{(x - 3)} + \frac{2x}{(x - 3)(x - 4)} - \frac{3(\frac{-(1 + 0)}{(x - 3)^{2}})x}{(x - 4)} - \frac{3(\frac{-(1 + 0)}{(x - 4)^{2}})x}{(x - 3)} - \frac{3}{(x - 3)(x - 4)} + \frac{2(\frac{-(1 + 0)}{(x - 3)^{2}})}{(x - 4)} + \frac{2(\frac{-(1 + 0)}{(x - 4)^{2}})}{(x - 3)})}{(\frac{x^{2}}{(x - 3)(x - 4)} - \frac{3x}{(x - 3)(x - 4)} + \frac{2}{(x - 3)(x - 4)})^{\frac{3}{2}}})x^{3}}{2(x - 4)^{2}(x - 3)} - \frac{(\frac{-2(1 + 0)}{(x - 4)^{3}})x^{3}}{2(\frac{x^{2}}{(x - 3)(x - 4)} - \frac{3x}{(x - 3)(x - 4)} + \frac{2}{(x - 3)(x - 4)})^{\frac{1}{2}}(x - 3)} - \frac{(\frac{-(1 + 0)}{(x - 3)^{2}})x^{3}}{2(\frac{x^{2}}{(x - 3)(x - 4)} - \frac{3x}{(x - 3)(x - 4)} + \frac{2}{(x - 3)(x - 4)})^{\frac{1}{2}}(x - 4)^{2}} - \frac{3x^{2}}{2(\frac{x^{2}}{(x - 3)(x - 4)} - \frac{3x}{(x - 3)(x - 4)} + \frac{2}{(x - 3)(x - 4)})^{\frac{1}{2}}(x - 4)^{2}(x - 3)} + \frac{(\frac{\frac{-1}{2}(\frac{(\frac{-(1 + 0)}{(x - 3)^{2}})x^{2}}{(x - 4)} + \frac{(\frac{-(1 + 0)}{(x - 4)^{2}})x^{2}}{(x - 3)} + \frac{2x}{(x - 3)(x - 4)} - \frac{3(\frac{-(1 + 0)}{(x - 3)^{2}})x}{(x - 4)} - \frac{3(\frac{-(1 + 0)}{(x - 4)^{2}})x}{(x - 3)} - \frac{3}{(x - 3)(x - 4)} + \frac{2(\frac{-(1 + 0)}{(x - 3)^{2}})}{(x - 4)} + \frac{2(\frac{-(1 + 0)}{(x - 4)^{2}})}{(x - 3)})}{(\frac{x^{2}}{(x - 3)(x - 4)} - \frac{3x}{(x - 3)(x - 4)} + \frac{2}{(x - 3)(x - 4)})^{\frac{3}{2}}})x^{2}}{(x - 4)(x - 3)} + \frac{(\frac{-(1 + 0)}{(x - 4)^{2}})x^{2}}{(\frac{x^{2}}{(x - 3)(x - 4)} - \frac{3x}{(x - 3)(x - 4)} + \frac{2}{(x - 3)(x - 4)})^{\frac{1}{2}}(x - 3)} + \frac{(\frac{-(1 + 0)}{(x - 3)^{2}})x^{2}}{(\frac{x^{2}}{(x - 3)(x - 4)} - \frac{3x}{(x - 3)(x - 4)} + \frac{2}{(x - 3)(x - 4)})^{\frac{1}{2}}(x - 4)} + \frac{2x}{(\frac{x^{2}}{(x - 3)(x - 4)} - \frac{3x}{(x - 3)(x - 4)} + \frac{2}{(x - 3)(x - 4)})^{\frac{1}{2}}(x - 4)(x - 3)} + \frac{3(\frac{\frac{-1}{2}(\frac{(\frac{-(1 + 0)}{(x - 3)^{2}})x^{2}}{(x - 4)} + \frac{(\frac{-(1 + 0)}{(x - 4)^{2}})x^{2}}{(x - 3)} + \frac{2x}{(x - 3)(x - 4)} - \frac{3(\frac{-(1 + 0)}{(x - 3)^{2}})x}{(x - 4)} - \frac{3(\frac{-(1 + 0)}{(x - 4)^{2}})x}{(x - 3)} - \frac{3}{(x - 3)(x - 4)} + \frac{2(\frac{-(1 + 0)}{(x - 3)^{2}})}{(x - 4)} + \frac{2(\frac{-(1 + 0)}{(x - 4)^{2}})}{(x - 3)})}{(\frac{x^{2}}{(x - 3)(x - 4)} - \frac{3x}{(x - 3)(x - 4)} + \frac{2}{(x - 3)(x - 4)})^{\frac{3}{2}}})x^{2}}{2(x - 3)^{2}(x - 4)} + \frac{3(\frac{-2(1 + 0)}{(x - 3)^{3}})x^{2}}{2(\frac{x^{2}}{(x - 3)(x - 4)} - \frac{3x}{(x - 3)(x - 4)} + \frac{2}{(x - 3)(x - 4)})^{\frac{1}{2}}(x - 4)} + \frac{3(\frac{-(1 + 0)}{(x - 4)^{2}})x^{2}}{2(\frac{x^{2}}{(x - 3)(x - 4)} - \frac{3x}{(x - 3)(x - 4)} + \frac{2}{(x - 3)(x - 4)})^{\frac{1}{2}}(x - 3)^{2}} + \frac{3*2x}{2(\frac{x^{2}}{(x - 3)(x - 4)} - \frac{3x}{(x - 3)(x - 4)} + \frac{2}{(x - 3)(x - 4)})^{\frac{1}{2}}(x - 3)^{2}(x - 4)} + \frac{3(\frac{\frac{-1}{2}(\frac{(\frac{-(1 + 0)}{(x - 3)^{2}})x^{2}}{(x - 4)} + \frac{(\frac{-(1 + 0)}{(x - 4)^{2}})x^{2}}{(x - 3)} + \frac{2x}{(x - 3)(x - 4)} - \frac{3(\frac{-(1 + 0)}{(x - 3)^{2}})x}{(x - 4)} - \frac{3(\frac{-(1 + 0)}{(x - 4)^{2}})x}{(x - 3)} - \frac{3}{(x - 3)(x - 4)} + \frac{2(\frac{-(1 + 0)}{(x - 3)^{2}})}{(x - 4)} + \frac{2(\frac{-(1 + 0)}{(x - 4)^{2}})}{(x - 3)})}{(\frac{x^{2}}{(x - 3)(x - 4)} - \frac{3x}{(x - 3)(x - 4)} + \frac{2}{(x - 3)(x - 4)})^{\frac{3}{2}}})x^{2}}{2(x - 4)^{2}(x - 3)} + \frac{3(\frac{-2(1 + 0)}{(x - 4)^{3}})x^{2}}{2(\frac{x^{2}}{(x - 3)(x - 4)} - \frac{3x}{(x - 3)(x - 4)} + \frac{2}{(x - 3)(x - 4)})^{\frac{1}{2}}(x - 3)} + \frac{3(\frac{-(1 + 0)}{(x - 3)^{2}})x^{2}}{2(\frac{x^{2}}{(x - 3)(x - 4)} - \frac{3x}{(x - 3)(x - 4)} + \frac{2}{(x - 3)(x - 4)})^{\frac{1}{2}}(x - 4)^{2}} + \frac{3*2x}{2(\frac{x^{2}}{(x - 3)(x - 4)} - \frac{3x}{(x - 3)(x - 4)} + \frac{2}{(x - 3)(x - 4)})^{\frac{1}{2}}(x - 4)^{2}(x - 3)} - \frac{3(\frac{\frac{-1}{2}(\frac{(\frac{-(1 + 0)}{(x - 3)^{2}})x^{2}}{(x - 4)} + \frac{(\frac{-(1 + 0)}{(x - 4)^{2}})x^{2}}{(x - 3)} + \frac{2x}{(x - 3)(x - 4)} - \frac{3(\frac{-(1 + 0)}{(x - 3)^{2}})x}{(x - 4)} - \frac{3(\frac{-(1 + 0)}{(x - 4)^{2}})x}{(x - 3)} - \frac{3}{(x - 3)(x - 4)} + \frac{2(\frac{-(1 + 0)}{(x - 3)^{2}})}{(x - 4)} + \frac{2(\frac{-(1 + 0)}{(x - 4)^{2}})}{(x - 3)})}{(\frac{x^{2}}{(x - 3)(x - 4)} - \frac{3x}{(x - 3)(x - 4)} + \frac{2}{(x - 3)(x - 4)})^{\frac{3}{2}}})x}{2(x - 3)(x - 4)} - \frac{3(\frac{-(1 + 0)}{(x - 3)^{2}})x}{2(\frac{x^{2}}{(x - 3)(x - 4)} - \frac{3x}{(x - 3)(x - 4)} + \frac{2}{(x - 3)(x - 4)})^{\frac{1}{2}}(x - 4)} - \frac{3(\frac{-(1 + 0)}{(x - 4)^{2}})x}{2(\frac{x^{2}}{(x - 3)(x - 4)} - \frac{3x}{(x - 3)(x - 4)} + \frac{2}{(x - 3)(x - 4)})^{\frac{1}{2}}(x - 3)} - \frac{3}{2(\frac{x^{2}}{(x - 3)(x - 4)} - \frac{3x}{(x - 3)(x - 4)} + \frac{2}{(x - 3)(x - 4)})^{\frac{1}{2}}(x - 3)(x - 4)} - \frac{(\frac{\frac{-1}{2}(\frac{(\frac{-(1 + 0)}{(x - 3)^{2}})x^{2}}{(x - 4)} + \frac{(\frac{-(1 + 0)}{(x - 4)^{2}})x^{2}}{(x - 3)} + \frac{2x}{(x - 3)(x - 4)} - \frac{3(\frac{-(1 + 0)}{(x - 3)^{2}})x}{(x - 4)} - \frac{3(\frac{-(1 + 0)}{(x - 4)^{2}})x}{(x - 3)} - \frac{3}{(x - 3)(x - 4)} + \frac{2(\frac{-(1 + 0)}{(x - 3)^{2}})}{(x - 4)} + \frac{2(\frac{-(1 + 0)}{(x - 4)^{2}})}{(x - 3)})}{(\frac{x^{2}}{(x - 3)(x - 4)} - \frac{3x}{(x - 3)(x - 4)} + \frac{2}{(x - 3)(x - 4)})^{\frac{3}{2}}})x}{(x - 3)^{2}(x - 4)} - \frac{(\frac{-2(1 + 0)}{(x - 3)^{3}})x}{(\frac{x^{2}}{(x - 3)(x - 4)} - \frac{3x}{(x - 3)(x - 4)} + \frac{2}{(x - 3)(x - 4)})^{\frac{1}{2}}(x - 4)} - \frac{(\frac{-(1 + 0)}{(x - 4)^{2}})x}{(\frac{x^{2}}{(x - 3)(x - 4)} - \frac{3x}{(x - 3)(x - 4)} + \frac{2}{(x - 3)(x - 4)})^{\frac{1}{2}}(x - 3)^{2}} - \frac{1}{(\frac{x^{2}}{(x - 3)(x - 4)} - \frac{3x}{(x - 3)(x - 4)} + \frac{2}{(x - 3)(x - 4)})^{\frac{1}{2}}(x - 3)^{2}(x - 4)} - \frac{(\frac{\frac{-1}{2}(\frac{(\frac{-(1 + 0)}{(x - 3)^{2}})x^{2}}{(x - 4)} + \frac{(\frac{-(1 + 0)}{(x - 4)^{2}})x^{2}}{(x - 3)} + \frac{2x}{(x - 3)(x - 4)} - \frac{3(\frac{-(1 + 0)}{(x - 3)^{2}})x}{(x - 4)} - \frac{3(\frac{-(1 + 0)}{(x - 4)^{2}})x}{(x - 3)} - \frac{3}{(x - 3)(x - 4)} + \frac{2(\frac{-(1 + 0)}{(x - 3)^{2}})}{(x - 4)} + \frac{2(\frac{-(1 + 0)}{(x - 4)^{2}})}{(x - 3)})}{(\frac{x^{2}}{(x - 3)(x - 4)} - \frac{3x}{(x - 3)(x - 4)} + \frac{2}{(x - 3)(x - 4)})^{\frac{3}{2}}})x}{(x - 4)^{2}(x - 3)} - \frac{(\frac{-2(1 + 0)}{(x - 4)^{3}})x}{(\frac{x^{2}}{(x - 3)(x - 4)} - \frac{3x}{(x - 3)(x - 4)} + \frac{2}{(x - 3)(x - 4)})^{\frac{1}{2}}(x - 3)} - \frac{(\frac{-(1 + 0)}{(x - 3)^{2}})x}{(\frac{x^{2}}{(x - 3)(x - 4)} - \frac{3x}{(x - 3)(x - 4)} + \frac{2}{(x - 3)(x - 4)})^{\frac{1}{2}}(x - 4)^{2}} - \frac{1}{(\frac{x^{2}}{(x - 3)(x - 4)} - \frac{3x}{(x - 3)(x - 4)} + \frac{2}{(x - 3)(x - 4)})^{\frac{1}{2}}(x - 4)^{2}(x - 3)} + (\frac{\frac{1}{2}(\frac{(\frac{-(1 + 0)}{(x - 3)^{2}})x^{2}}{(x - 4)} + \frac{(\frac{-(1 + 0)}{(x - 4)^{2}})x^{2}}{(x - 3)} + \frac{2x}{(x - 3)(x - 4)} - \frac{3(\frac{-(1 + 0)}{(x - 3)^{2}})x}{(x - 4)} - \frac{3(\frac{-(1 + 0)}{(x - 4)^{2}})x}{(x - 3)} - \frac{3}{(x - 3)(x - 4)} + \frac{2(\frac{-(1 + 0)}{(x - 3)^{2}})}{(x - 4)} + \frac{2(\frac{-(1 + 0)}{(x - 4)^{2}})}{(x - 3)})}{(\frac{x^{2}}{(x - 3)(x - 4)} - \frac{3x}{(x - 3)(x - 4)} + \frac{2}{(x - 3)(x - 4)})^{\frac{1}{2}}})\\=&\frac{-x^{5}}{4(\frac{x^{2}}{(x - 3)(x - 4)} - \frac{3x}{(x - 3)(x - 4)} + \frac{2}{(x - 3)(x - 4)})^{\frac{3}{2}}(x - 3)^{4}(x - 4)^{2}} - \frac{x^{5}}{4(\frac{x^{2}}{(x - 3)(x - 4)} - \frac{3x}{(x - 3)(x - 4)} + \frac{2}{(x - 3)(x - 4)})^{\frac{3}{2}}(x - 4)^{3}(x - 3)^{3}} + \frac{x^{4}}{2(\frac{x^{2}}{(x - 3)(x - 4)} - \frac{3x}{(x - 3)(x - 4)} + \frac{2}{(x - 3)(x - 4)})^{\frac{3}{2}}(x - 4)^{2}(x - 3)^{3}} + \frac{3x^{4}}{2(\frac{x^{2}}{(x - 3)(x - 4)} - \frac{3x}{(x - 3)(x - 4)} + \frac{2}{(x - 3)(x - 4)})^{\frac{3}{2}}(x - 3)^{4}(x - 4)^{2}} + \frac{3x^{4}}{2(\frac{x^{2}}{(x - 3)(x - 4)} - \frac{3x}{(x - 3)(x - 4)} + \frac{2}{(x - 3)(x - 4)})^{\frac{3}{2}}(x - 4)^{3}(x - 3)^{3}} + \frac{x^{4}}{(\frac{x^{2}}{(x - 3)(x - 4)} - \frac{3x}{(x - 3)(x - 4)} + \frac{2}{(x - 3)(x - 4)})^{\frac{3}{2}}(x - 4)^{3}(x - 3)^{2}} - \frac{x^{5}}{4(\frac{x^{2}}{(x - 3)(x - 4)} - \frac{3x}{(x - 3)(x - 4)} + \frac{2}{(x - 3)(x - 4)})^{\frac{3}{2}}(x - 3)^{3}(x - 4)^{3}} - \frac{x^{5}}{4(\frac{x^{2}}{(x - 3)(x - 4)} - \frac{3x}{(x - 3)(x - 4)} + \frac{2}{(x - 3)(x - 4)})^{\frac{3}{2}}(x - 4)^{4}(x - 3)^{2}} + \frac{x^{3}}{(x - 3)^{3}(\frac{x^{2}}{(x - 3)(x - 4)} - \frac{3x}{(x - 3)(x - 4)} + \frac{2}{(x - 3)(x - 4)})^{\frac{1}{2}}(x - 4)} + \frac{x^{3}}{2(\frac{x^{2}}{(x - 3)(x - 4)} - \frac{3x}{(x - 3)(x - 4)} + \frac{2}{(x - 3)(x - 4)})^{\frac{1}{2}}(x - 4)^{2}(x - 3)^{2}} - \frac{3x^{2}}{2(x - 3)^{2}(x - 4)(\frac{x^{2}}{(x - 3)(x - 4)} - \frac{3x}{(x - 3)(x - 4)} + \frac{2}{(x - 3)(x - 4)})^{\frac{1}{2}}} + \frac{3x^{4}}{2(\frac{x^{2}}{(x - 3)(x - 4)} - \frac{3x}{(x - 3)(x - 4)} + \frac{2}{(x - 3)(x - 4)})^{\frac{3}{2}}(x - 3)^{3}(x - 4)^{3}} + \frac{3x^{4}}{2(\frac{x^{2}}{(x - 3)(x - 4)} - \frac{3x}{(x - 3)(x - 4)} + \frac{2}{(x - 3)(x - 4)})^{\frac{3}{2}}(x - 4)^{4}(x - 3)^{2}} + \frac{x^{4}}{2(\frac{x^{2}}{(x - 3)(x - 4)} - \frac{3x}{(x - 3)(x - 4)} + \frac{2}{(x - 3)(x - 4)})^{\frac{3}{2}}(x - 3)^{3}(x - 4)^{2}} - \frac{13x^{3}}{4(\frac{x^{2}}{(x - 3)(x - 4)} - \frac{3x}{(x - 3)(x - 4)} + \frac{2}{(x - 3)(x - 4)})^{\frac{3}{2}}(x - 3)^{4}(x - 4)^{2}} - \frac{13x^{3}}{4(\frac{x^{2}}{(x - 3)(x - 4)} - \frac{3x}{(x - 3)(x - 4)} + \frac{2}{(x - 3)(x - 4)})^{\frac{3}{2}}(x - 4)^{3}(x - 3)^{3}} + \frac{x^{3}}{(x - 4)^{3}(\frac{x^{2}}{(x - 3)(x - 4)} - \frac{3x}{(x - 3)(x - 4)} + \frac{2}{(x - 3)(x - 4)})^{\frac{1}{2}}(x - 3)} + \frac{x^{3}}{2(\frac{x^{2}}{(x - 3)(x - 4)} - \frac{3x}{(x - 3)(x - 4)} + \frac{2}{(x - 3)(x - 4)})^{\frac{1}{2}}(x - 3)^{2}(x - 4)^{2}} - \frac{3x^{2}}{2(x - 4)^{2}(x - 3)(\frac{x^{2}}{(x - 3)(x - 4)} - \frac{3x}{(x - 3)(x - 4)} + \frac{2}{(x - 3)(x - 4)})^{\frac{1}{2}}} - \frac{3x^{3}}{(\frac{x^{2}}{(x - 3)(x - 4)} - \frac{3x}{(x - 3)(x - 4)} + \frac{2}{(x - 3)(x - 4)})^{\frac{3}{2}}(x - 3)^{3}(x - 4)^{2}} - \frac{15x^{3}}{4(\frac{x^{2}}{(x - 3)(x - 4)} - \frac{3x}{(x - 3)(x - 4)} + \frac{2}{(x - 3)(x - 4)})^{\frac{3}{2}}(x - 4)^{3}(x - 3)^{2}} - \frac{x^{3}}{(\frac{x^{2}}{(x - 3)(x - 4)} - \frac{3x}{(x - 3)(x - 4)} + \frac{2}{(x - 3)(x - 4)})^{\frac{3}{2}}(x - 4)^{2}(x - 3)^{2}} - \frac{3x^{3}}{2(\frac{x^{2}}{(x - 3)(x - 4)} - \frac{3x}{(x - 3)(x - 4)} + \frac{2}{(x - 3)(x - 4)})^{\frac{3}{2}}(x - 4)^{2}(x - 3)^{3}} + \frac{3x^{2}}{2(\frac{x^{2}}{(x - 3)(x - 4)} - \frac{3x}{(x - 3)(x - 4)} + \frac{2}{(x - 3)(x - 4)})^{\frac{3}{2}}(x - 4)^{2}(x - 3)^{2}} - \frac{x^{2}}{(x - 4)^{2}(\frac{x^{2}}{(x - 3)(x - 4)} - \frac{3x}{(x - 3)(x - 4)} + \frac{2}{(x - 3)(x - 4)})^{\frac{1}{2}}(x - 3)} - \frac{3x^{2}}{2(\frac{x^{2}}{(x - 3)(x - 4)} - \frac{3x}{(x - 3)(x - 4)} + \frac{2}{(x - 3)(x - 4)})^{\frac{1}{2}}(x - 3)^{2}(x - 4)} + \frac{2x}{(x - 4)(x - 3)(\frac{x^{2}}{(x - 3)(x - 4)} - \frac{3x}{(x - 3)(x - 4)} + \frac{2}{(x - 3)(x - 4)})^{\frac{1}{2}}} + \frac{11x^{2}}{2(\frac{x^{2}}{(x - 3)(x - 4)} - \frac{3x}{(x - 3)(x - 4)} + \frac{2}{(x - 3)(x - 4)})^{\frac{3}{2}}(x - 3)^{3}(x - 4)^{2}} - \frac{13x^{3}}{4(\frac{x^{2}}{(x - 3)(x - 4)} - \frac{3x}{(x - 3)(x - 4)} + \frac{2}{(x - 3)(x - 4)})^{\frac{3}{2}}(x - 3)^{3}(x - 4)^{3}} - \frac{13x^{3}}{4(\frac{x^{2}}{(x - 3)(x - 4)} - \frac{3x}{(x - 3)(x - 4)} + \frac{2}{(x - 3)(x - 4)})^{\frac{3}{2}}(x - 4)^{4}(x - 3)^{2}} + \frac{17x^{2}}{4(\frac{x^{2}}{(x - 3)(x - 4)} - \frac{3x}{(x - 3)(x - 4)} + \frac{2}{(x - 3)(x - 4)})^{\frac{3}{2}}(x - 4)^{3}(x - 3)^{2}} - \frac{3x^{2}}{(x - 3)^{3}(\frac{x^{2}}{(x - 3)(x - 4)} - \frac{3x}{(x - 3)(x - 4)} + \frac{2}{(x - 3)(x - 4)})^{\frac{1}{2}}(x - 4)} - \frac{3x^{2}}{2(\frac{x^{2}}{(x - 3)(x - 4)} - \frac{3x}{(x - 3)(x - 4)} + \frac{2}{(x - 3)(x - 4)})^{\frac{1}{2}}(x - 4)^{2}(x - 3)^{2}} + \frac{3x}{(x - 3)^{2}(x - 4)(\frac{x^{2}}{(x - 3)(x - 4)} - \frac{3x}{(x - 3)(x - 4)} + \frac{2}{(x - 3)(x - 4)})^{\frac{1}{2}}} + \frac{3x^{2}}{(\frac{x^{2}}{(x - 3)(x - 4)} - \frac{3x}{(x - 3)(x - 4)} + \frac{2}{(x - 3)(x - 4)})^{\frac{3}{2}}(x - 3)^{4}(x - 4)^{2}} + \frac{3x^{2}}{(\frac{x^{2}}{(x - 3)(x - 4)} - \frac{3x}{(x - 3)(x - 4)} + \frac{2}{(x - 3)(x - 4)})^{\frac{3}{2}}(x - 4)^{3}(x - 3)^{3}} + \frac{x^{2}}{(\frac{x^{2}}{(x - 3)(x - 4)} - \frac{3x}{(x - 3)(x - 4)} + \frac{2}{(x - 3)(x - 4)})^{\frac{3}{2}}(x - 4)^{2}(x - 3)^{3}} + \frac{3x^{2}}{(\frac{x^{2}}{(x - 3)(x - 4)} - \frac{3x}{(x - 3)(x - 4)} + \frac{2}{(x - 3)(x - 4)})^{\frac{3}{2}}(x - 3)^{3}(x - 4)^{3}} + \frac{3x^{2}}{(\frac{x^{2}}{(x - 3)(x - 4)} - \frac{3x}{(x - 3)(x - 4)} + \frac{2}{(x - 3)(x - 4)})^{\frac{3}{2}}(x - 4)^{4}(x - 3)^{2}} - \frac{3x^{2}}{(x - 4)^{3}(\frac{x^{2}}{(x - 3)(x - 4)} - \frac{3x}{(x - 3)(x - 4)} + \frac{2}{(x - 3)(x - 4)})^{\frac{1}{2}}(x - 3)} - \frac{3x^{2}}{2(\frac{x^{2}}{(x - 3)(x - 4)} - \frac{3x}{(x - 3)(x - 4)} + \frac{2}{(x - 3)(x - 4)})^{\frac{1}{2}}(x - 3)^{2}(x - 4)^{2}} + \frac{3x}{(x - 4)^{2}(x - 3)(\frac{x^{2}}{(x - 3)(x - 4)} - \frac{3x}{(x - 3)(x - 4)} + \frac{2}{(x - 3)(x - 4)})^{\frac{1}{2}}} + \frac{3x^{2}}{2(\frac{x^{2}}{(x - 3)(x - 4)} - \frac{3x}{(x - 3)(x - 4)} + \frac{2}{(x - 3)(x - 4)})^{\frac{3}{2}}(x - 3)^{2}(x - 4)^{2}} - \frac{9x}{4(\frac{x^{2}}{(x - 3)(x - 4)} - \frac{3x}{(x - 3)(x - 4)} + \frac{2}{(x - 3)(x - 4)})^{\frac{3}{2}}(x - 3)^{2}(x - 4)^{2}} - \frac{3x}{(\frac{x^{2}}{(x - 3)(x - 4)} - \frac{3x}{(x - 3)(x - 4)} + \frac{2}{(x - 3)(x - 4)})^{\frac{3}{2}}(x - 3)^{3}(x - 4)^{2}} - \frac{3x}{2(\frac{x^{2}}{(x - 3)(x - 4)} - \frac{3x}{(x - 3)(x - 4)} + \frac{2}{(x - 3)(x - 4)})^{\frac{3}{2}}(x - 4)^{3}(x - 3)^{2}} + \frac{3x}{2(x - 3)^{2}(\frac{x^{2}}{(x - 3)(x - 4)} - \frac{3x}{(x - 3)(x - 4)} + \frac{2}{(x - 3)(x - 4)})^{\frac{1}{2}}(x - 4)} + \frac{3x}{(\frac{x^{2}}{(x - 3)(x - 4)} - \frac{3x}{(x - 3)(x - 4)} + \frac{2}{(x - 3)(x - 4)})^{\frac{1}{2}}(x - 4)^{2}(x - 3)} - \frac{3x^{3}}{4(\frac{x^{2}}{(x - 3)(x - 4)} - \frac{3x}{(x - 3)(x - 4)} + \frac{2}{(x - 3)(x - 4)})^{\frac{3}{2}}(x - 3)^{2}(x - 4)^{3}} - \frac{x}{(\frac{x^{2}}{(x - 3)(x - 4)} - \frac{3x}{(x - 3)(x - 4)} + \frac{2}{(x - 3)(x - 4)})^{\frac{3}{2}}(x - 3)^{4}(x - 4)^{2}} - \frac{x}{(\frac{x^{2}}{(x - 3)(x - 4)} - \frac{3x}{(x - 3)(x - 4)} + \frac{2}{(x - 3)(x - 4)})^{\frac{3}{2}}(x - 4)^{3}(x - 3)^{3}} + \frac{9x^{2}}{4(\frac{x^{2}}{(x - 3)(x - 4)} - \frac{3x}{(x - 3)(x - 4)} + \frac{2}{(x - 3)(x - 4)})^{\frac{3}{2}}(x - 3)^{2}(x - 4)^{3}} - \frac{3x}{2(\frac{x^{2}}{(x - 3)(x - 4)} - \frac{3x}{(x - 3)(x - 4)} + \frac{2}{(x - 3)(x - 4)})^{\frac{3}{2}}(x - 3)^{2}(x - 4)^{3}} - \frac{x}{(\frac{x^{2}}{(x - 3)(x - 4)} - \frac{3x}{(x - 3)(x - 4)} + \frac{2}{(x - 3)(x - 4)})^{\frac{3}{2}}(x - 3)^{3}(x - 4)^{3}} - \frac{x}{(\frac{x^{2}}{(x - 3)(x - 4)} - \frac{3x}{(x - 3)(x - 4)} + \frac{2}{(x - 3)(x - 4)})^{\frac{3}{2}}(x - 4)^{4}(x - 3)^{2}} + \frac{2x}{(x - 3)^{3}(\frac{x^{2}}{(x - 3)(x - 4)} - \frac{3x}{(x - 3)(x - 4)} + \frac{2}{(x - 3)(x - 4)})^{\frac{1}{2}}(x - 4)} + \frac{x}{(\frac{x^{2}}{(x - 3)(x - 4)} - \frac{3x}{(x - 3)(x - 4)} + \frac{2}{(x - 3)(x - 4)})^{\frac{1}{2}}(x - 4)^{2}(x - 3)^{2}} + \frac{2x}{(x - 4)^{3}(\frac{x^{2}}{(x - 3)(x - 4)} - \frac{3x}{(x - 3)(x - 4)} + \frac{2}{(x - 3)(x - 4)})^{\frac{1}{2}}(x - 3)} + \frac{x}{(\frac{x^{2}}{(x - 3)(x - 4)} - \frac{3x}{(x - 3)(x - 4)} + \frac{2}{(x - 3)(x - 4)})^{\frac{1}{2}}(x - 3)^{2}(x - 4)^{2}} - \frac{x^{2}}{2(\frac{x^{2}}{(x - 3)(x - 4)} - \frac{3x}{(x - 3)(x - 4)} + \frac{2}{(x - 3)(x - 4)})^{\frac{1}{2}}(x - 4)^{2}(x - 3)} + \frac{x}{(\frac{x^{2}}{(x - 3)(x - 4)} - \frac{3x}{(x - 3)(x - 4)} + \frac{2}{(x - 3)(x - 4)})^{\frac{1}{2}}(x - 4)(x - 3)} + \frac{3x}{2(\frac{x^{2}}{(x - 3)(x - 4)} - \frac{3x}{(x - 3)(x - 4)} + \frac{2}{(x - 3)(x - 4)})^{\frac{1}{2}}(x - 3)^{2}(x - 4)} - \frac{2}{(\frac{x^{2}}{(x - 3)(x - 4)} - \frac{3x}{(x - 3)(x - 4)} + \frac{2}{(x - 3)(x - 4)})^{\frac{1}{2}}(x - 3)^{2}(x - 4)} - \frac{2}{(\frac{x^{2}}{(x - 3)(x - 4)} - \frac{3x}{(x - 3)(x - 4)} + \frac{2}{(x - 3)(x - 4)})^{\frac{1}{2}}(x - 4)^{2}(x - 3)} - \frac{3}{(\frac{x^{2}}{(x - 3)(x - 4)} - \frac{3x}{(x - 3)(x - 4)} + \frac{2}{(x - 3)(x - 4)})^{\frac{1}{2}}(x - 3)(x - 4)}\\ \end{split}\end{equation} \]



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