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。
\[ \begin{equation}\begin{split}【1/1】求函数\frac{(xA + (1 - x)B - D)}{sqrt(({x}^{2})({A}^{2}) + ({(1 - x)}^{2}){B}^{2} + 2Cx(1 - x)AB)} 关于 x 的 1 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = \frac{Ax}{sqrt(A^{2}x^{2} + B^{2}x^{2} - 2B^{2}x + B^{2} + 2ABCx - 2ABCx^{2})} + \frac{B}{sqrt(A^{2}x^{2} + B^{2}x^{2} - 2B^{2}x + B^{2} + 2ABCx - 2ABCx^{2})} - \frac{Bx}{sqrt(A^{2}x^{2} + B^{2}x^{2} - 2B^{2}x + B^{2} + 2ABCx - 2ABCx^{2})} - \frac{D}{sqrt(A^{2}x^{2} + B^{2}x^{2} - 2B^{2}x + B^{2} + 2ABCx - 2ABCx^{2})}\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( \frac{Ax}{sqrt(A^{2}x^{2} + B^{2}x^{2} - 2B^{2}x + B^{2} + 2ABCx - 2ABCx^{2})} + \frac{B}{sqrt(A^{2}x^{2} + B^{2}x^{2} - 2B^{2}x + B^{2} + 2ABCx - 2ABCx^{2})} - \frac{Bx}{sqrt(A^{2}x^{2} + B^{2}x^{2} - 2B^{2}x + B^{2} + 2ABCx - 2ABCx^{2})} - \frac{D}{sqrt(A^{2}x^{2} + B^{2}x^{2} - 2B^{2}x + B^{2} + 2ABCx - 2ABCx^{2})}\right)}{dx}\\=&\frac{A}{sqrt(A^{2}x^{2} + B^{2}x^{2} - 2B^{2}x + B^{2} + 2ABCx - 2ABCx^{2})} + \frac{Ax*-(A^{2}*2x + B^{2}*2x - 2B^{2} + 0 + 2ABC - 2ABC*2x)*\frac{1}{2}}{(A^{2}x^{2} + B^{2}x^{2} - 2B^{2}x + B^{2} + 2ABCx - 2ABCx^{2})(A^{2}x^{2} + B^{2}x^{2} - 2B^{2}x + B^{2} + 2ABCx - 2ABCx^{2})^{\frac{1}{2}}} + \frac{B*-(A^{2}*2x + B^{2}*2x - 2B^{2} + 0 + 2ABC - 2ABC*2x)*\frac{1}{2}}{(A^{2}x^{2} + B^{2}x^{2} - 2B^{2}x + B^{2} + 2ABCx - 2ABCx^{2})(A^{2}x^{2} + B^{2}x^{2} - 2B^{2}x + B^{2} + 2ABCx - 2ABCx^{2})^{\frac{1}{2}}} - \frac{B}{sqrt(A^{2}x^{2} + B^{2}x^{2} - 2B^{2}x + B^{2} + 2ABCx - 2ABCx^{2})} - \frac{Bx*-(A^{2}*2x + B^{2}*2x - 2B^{2} + 0 + 2ABC - 2ABC*2x)*\frac{1}{2}}{(A^{2}x^{2} + B^{2}x^{2} - 2B^{2}x + B^{2} + 2ABCx - 2ABCx^{2})(A^{2}x^{2} + B^{2}x^{2} - 2B^{2}x + B^{2} + 2ABCx - 2ABCx^{2})^{\frac{1}{2}}} - \frac{D*-(A^{2}*2x + B^{2}*2x - 2B^{2} + 0 + 2ABC - 2ABC*2x)*\frac{1}{2}}{(A^{2}x^{2} + B^{2}x^{2} - 2B^{2}x + B^{2} + 2ABCx - 2ABCx^{2})(A^{2}x^{2} + B^{2}x^{2} - 2B^{2}x + B^{2} + 2ABCx - 2ABCx^{2})^{\frac{1}{2}}}\\=&\frac{A}{sqrt(A^{2}x^{2} + B^{2}x^{2} - 2B^{2}x + B^{2} + 2ABCx - 2ABCx^{2})} - \frac{A^{3}x^{2}}{(A^{2}x^{2} + B^{2}x^{2} - 2B^{2}x + B^{2} + 2ABCx - 2ABCx^{2})^{\frac{3}{2}}} - \frac{AB^{2}x^{2}}{(A^{2}x^{2} + B^{2}x^{2} - 2B^{2}x + B^{2} + 2ABCx - 2ABCx^{2})^{\frac{3}{2}}} + \frac{AB^{2}x}{(A^{2}x^{2} + B^{2}x^{2} - 2B^{2}x + B^{2} + 2ABCx - 2ABCx^{2})^{\frac{3}{2}}} - \frac{A^{2}BCx}{(A^{2}x^{2} + B^{2}x^{2} - 2B^{2}x + B^{2} + 2ABCx - 2ABCx^{2})^{\frac{3}{2}}} + \frac{2A^{2}BCx^{2}}{(A^{2}x^{2} + B^{2}x^{2} - 2B^{2}x + B^{2} + 2ABCx - 2ABCx^{2})^{\frac{3}{2}}} + \frac{A^{2}Bx^{2}}{(A^{2}x^{2} + B^{2}x^{2} - 2B^{2}x + B^{2} + 2ABCx - 2ABCx^{2})^{\frac{3}{2}}} + \frac{B^{3}x^{2}}{(A^{2}x^{2} + B^{2}x^{2} - 2B^{2}x + B^{2} + 2ABCx - 2ABCx^{2})^{\frac{3}{2}}} - \frac{2B^{3}x}{(A^{2}x^{2} + B^{2}x^{2} - 2B^{2}x + B^{2} + 2ABCx - 2ABCx^{2})^{\frac{3}{2}}} + \frac{3AB^{2}Cx}{(A^{2}x^{2} + B^{2}x^{2} - 2B^{2}x + B^{2} + 2ABCx - 2ABCx^{2})^{\frac{3}{2}}} - \frac{2AB^{2}Cx^{2}}{(A^{2}x^{2} + B^{2}x^{2} - 2B^{2}x + B^{2} + 2ABCx - 2ABCx^{2})^{\frac{3}{2}}} - \frac{B}{sqrt(A^{2}x^{2} + B^{2}x^{2} - 2B^{2}x + B^{2} + 2ABCx - 2ABCx^{2})} - \frac{A^{2}Bx}{(A^{2}x^{2} + B^{2}x^{2} - 2B^{2}x + B^{2} + 2ABCx - 2ABCx^{2})^{\frac{3}{2}}} + \frac{B^{2}Dx}{(A^{2}x^{2} + B^{2}x^{2} - 2B^{2}x + B^{2} + 2ABCx - 2ABCx^{2})^{\frac{3}{2}}} - \frac{AB^{2}C}{(A^{2}x^{2} + B^{2}x^{2} - 2B^{2}x + B^{2} + 2ABCx - 2ABCx^{2})^{\frac{3}{2}}} + \frac{A^{2}Dx}{(A^{2}x^{2} + B^{2}x^{2} - 2B^{2}x + B^{2} + 2ABCx - 2ABCx^{2})^{\frac{3}{2}}} - \frac{B^{2}D}{(A^{2}x^{2} + B^{2}x^{2} - 2B^{2}x + B^{2} + 2ABCx - 2ABCx^{2})^{\frac{3}{2}}} + \frac{B^{3}}{(A^{2}x^{2} + B^{2}x^{2} - 2B^{2}x + B^{2} + 2ABCx - 2ABCx^{2})^{\frac{3}{2}}} - \frac{2ABDCx}{(A^{2}x^{2} + B^{2}x^{2} - 2B^{2}x + B^{2} + 2ABCx - 2ABCx^{2})^{\frac{3}{2}}} + \frac{ABDC}{(A^{2}x^{2} + B^{2}x^{2} - 2B^{2}x + B^{2} + 2ABCx - 2ABCx^{2})^{\frac{3}{2}}}\\ \end{split}\end{equation} \]
注意，变量是区分大小写的。
\[ \begin{equation}\begin{split}【1/1】求函数\frac{(xA + (1 - x)B - D)}{sqrt(({x}^{2})({A}^{2}) + ({(1 - x)}^{2}){B}^{2} + 2Cx(1 - x)AB)} 关于 x 的 1 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = \frac{Ax}{sqrt(A^{2}x^{2} + B^{2}x^{2} - 2B^{2}x + B^{2} + 2ABCx - 2ABCx^{2})} + \frac{B}{sqrt(A^{2}x^{2} + B^{2}x^{2} - 2B^{2}x + B^{2} + 2ABCx - 2ABCx^{2})} - \frac{Bx}{sqrt(A^{2}x^{2} + B^{2}x^{2} - 2B^{2}x + B^{2} + 2ABCx - 2ABCx^{2})} - \frac{D}{sqrt(A^{2}x^{2} + B^{2}x^{2} - 2B^{2}x + B^{2} + 2ABCx - 2ABCx^{2})}\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( \frac{Ax}{sqrt(A^{2}x^{2} + B^{2}x^{2} - 2B^{2}x + B^{2} + 2ABCx - 2ABCx^{2})} + \frac{B}{sqrt(A^{2}x^{2} + B^{2}x^{2} - 2B^{2}x + B^{2} + 2ABCx - 2ABCx^{2})} - \frac{Bx}{sqrt(A^{2}x^{2} + B^{2}x^{2} - 2B^{2}x + B^{2} + 2ABCx - 2ABCx^{2})} - \frac{D}{sqrt(A^{2}x^{2} + B^{2}x^{2} - 2B^{2}x + B^{2} + 2ABCx - 2ABCx^{2})}\right)}{dx}\\=&\frac{A}{sqrt(A^{2}x^{2} + B^{2}x^{2} - 2B^{2}x + B^{2} + 2ABCx - 2ABCx^{2})} + \frac{Ax*-(A^{2}*2x + B^{2}*2x - 2B^{2} + 0 + 2ABC - 2ABC*2x)*\frac{1}{2}}{(A^{2}x^{2} + B^{2}x^{2} - 2B^{2}x + B^{2} + 2ABCx - 2ABCx^{2})(A^{2}x^{2} + B^{2}x^{2} - 2B^{2}x + B^{2} + 2ABCx - 2ABCx^{2})^{\frac{1}{2}}} + \frac{B*-(A^{2}*2x + B^{2}*2x - 2B^{2} + 0 + 2ABC - 2ABC*2x)*\frac{1}{2}}{(A^{2}x^{2} + B^{2}x^{2} - 2B^{2}x + B^{2} + 2ABCx - 2ABCx^{2})(A^{2}x^{2} + B^{2}x^{2} - 2B^{2}x + B^{2} + 2ABCx - 2ABCx^{2})^{\frac{1}{2}}} - \frac{B}{sqrt(A^{2}x^{2} + B^{2}x^{2} - 2B^{2}x + B^{2} + 2ABCx - 2ABCx^{2})} - \frac{Bx*-(A^{2}*2x + B^{2}*2x - 2B^{2} + 0 + 2ABC - 2ABC*2x)*\frac{1}{2}}{(A^{2}x^{2} + B^{2}x^{2} - 2B^{2}x + B^{2} + 2ABCx - 2ABCx^{2})(A^{2}x^{2} + B^{2}x^{2} - 2B^{2}x + B^{2} + 2ABCx - 2ABCx^{2})^{\frac{1}{2}}} - \frac{D*-(A^{2}*2x + B^{2}*2x - 2B^{2} + 0 + 2ABC - 2ABC*2x)*\frac{1}{2}}{(A^{2}x^{2} + B^{2}x^{2} - 2B^{2}x + B^{2} + 2ABCx - 2ABCx^{2})(A^{2}x^{2} + B^{2}x^{2} - 2B^{2}x + B^{2} + 2ABCx - 2ABCx^{2})^{\frac{1}{2}}}\\=&\frac{A}{sqrt(A^{2}x^{2} + B^{2}x^{2} - 2B^{2}x + B^{2} + 2ABCx - 2ABCx^{2})} - \frac{A^{3}x^{2}}{(A^{2}x^{2} + B^{2}x^{2} - 2B^{2}x + B^{2} + 2ABCx - 2ABCx^{2})^{\frac{3}{2}}} - \frac{AB^{2}x^{2}}{(A^{2}x^{2} + B^{2}x^{2} - 2B^{2}x + B^{2} + 2ABCx - 2ABCx^{2})^{\frac{3}{2}}} + \frac{AB^{2}x}{(A^{2}x^{2} + B^{2}x^{2} - 2B^{2}x + B^{2} + 2ABCx - 2ABCx^{2})^{\frac{3}{2}}} - \frac{A^{2}BCx}{(A^{2}x^{2} + B^{2}x^{2} - 2B^{2}x + B^{2} + 2ABCx - 2ABCx^{2})^{\frac{3}{2}}} + \frac{2A^{2}BCx^{2}}{(A^{2}x^{2} + B^{2}x^{2} - 2B^{2}x + B^{2} + 2ABCx - 2ABCx^{2})^{\frac{3}{2}}} + \frac{A^{2}Bx^{2}}{(A^{2}x^{2} + B^{2}x^{2} - 2B^{2}x + B^{2} + 2ABCx - 2ABCx^{2})^{\frac{3}{2}}} + \frac{B^{3}x^{2}}{(A^{2}x^{2} + B^{2}x^{2} - 2B^{2}x + B^{2} + 2ABCx - 2ABCx^{2})^{\frac{3}{2}}} - \frac{2B^{3}x}{(A^{2}x^{2} + B^{2}x^{2} - 2B^{2}x + B^{2} + 2ABCx - 2ABCx^{2})^{\frac{3}{2}}} + \frac{3AB^{2}Cx}{(A^{2}x^{2} + B^{2}x^{2} - 2B^{2}x + B^{2} + 2ABCx - 2ABCx^{2})^{\frac{3}{2}}} - \frac{2AB^{2}Cx^{2}}{(A^{2}x^{2} + B^{2}x^{2} - 2B^{2}x + B^{2} + 2ABCx - 2ABCx^{2})^{\frac{3}{2}}} - \frac{B}{sqrt(A^{2}x^{2} + B^{2}x^{2} - 2B^{2}x + B^{2} + 2ABCx - 2ABCx^{2})} - \frac{A^{2}Bx}{(A^{2}x^{2} + B^{2}x^{2} - 2B^{2}x + B^{2} + 2ABCx - 2ABCx^{2})^{\frac{3}{2}}} + \frac{B^{2}Dx}{(A^{2}x^{2} + B^{2}x^{2} - 2B^{2}x + B^{2} + 2ABCx - 2ABCx^{2})^{\frac{3}{2}}} - \frac{AB^{2}C}{(A^{2}x^{2} + B^{2}x^{2} - 2B^{2}x + B^{2} + 2ABCx - 2ABCx^{2})^{\frac{3}{2}}} + \frac{A^{2}Dx}{(A^{2}x^{2} + B^{2}x^{2} - 2B^{2}x + B^{2} + 2ABCx - 2ABCx^{2})^{\frac{3}{2}}} - \frac{B^{2}D}{(A^{2}x^{2} + B^{2}x^{2} - 2B^{2}x + B^{2} + 2ABCx - 2ABCx^{2})^{\frac{3}{2}}} + \frac{B^{3}}{(A^{2}x^{2} + B^{2}x^{2} - 2B^{2}x + B^{2} + 2ABCx - 2ABCx^{2})^{\frac{3}{2}}} - \frac{2ABDCx}{(A^{2}x^{2} + B^{2}x^{2} - 2B^{2}x + B^{2} + 2ABCx - 2ABCx^{2})^{\frac{3}{2}}} + \frac{ABDC}{(A^{2}x^{2} + B^{2}x^{2} - 2B^{2}x + B^{2} + 2ABCx - 2ABCx^{2})^{\frac{3}{2}}}\\ \end{split}\end{equation} \]
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