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。
\[ \begin{equation}\begin{split}【1/1】求函数\frac{(xA + (1 - x)B - 0.08)}{sqrt(({x}^{2})({A}^{2}) + ({(1 - x)}^{2}){B}^{2} + 0.8x(1 - x)AB)} 关于 x 的 1 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = \frac{Ax}{sqrt(Ax - Bx + B + 0.8ABx - 0.8ABx^{2})} + \frac{B}{sqrt(Ax - Bx + B + 0.8ABx - 0.8ABx^{2})} - \frac{Bx}{sqrt(Ax - Bx + B + 0.8ABx - 0.8ABx^{2})} - \frac{0.08}{sqrt(Ax - Bx + B + 0.8ABx - 0.8ABx^{2})}\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( \frac{Ax}{sqrt(Ax - Bx + B + 0.8ABx - 0.8ABx^{2})} + \frac{B}{sqrt(Ax - Bx + B + 0.8ABx - 0.8ABx^{2})} - \frac{Bx}{sqrt(Ax - Bx + B + 0.8ABx - 0.8ABx^{2})} - \frac{0.08}{sqrt(Ax - Bx + B + 0.8ABx - 0.8ABx^{2})}\right)}{dx}\\=&\frac{A}{sqrt(Ax - Bx + B + 0.8ABx - 0.8ABx^{2})} - \frac{Ax(A - B + 0 + 0.8AB - 0.8AB*2x)*0.5}{(Ax - Bx + B + 0.8ABx - 0.8ABx^{2})(Ax - Bx + B + 0.8ABx - 0.8ABx^{2})^{\frac{1}{2}}} + \frac{B*-(A - B + 0 + 0.8AB - 0.8AB*2x)*0.5}{(Ax - Bx + B + 0.8ABx - 0.8ABx^{2})(Ax - Bx + B + 0.8ABx - 0.8ABx^{2})^{\frac{1}{2}}} - \frac{B}{sqrt(Ax - Bx + B + 0.8ABx - 0.8ABx^{2})} + \frac{Bx(A - B + 0 + 0.8AB - 0.8AB*2x)*0.5}{(Ax - Bx + B + 0.8ABx - 0.8ABx^{2})(Ax - Bx + B + 0.8ABx - 0.8ABx^{2})^{\frac{1}{2}}} - \frac{0.08*-(A - B + 0 + 0.8AB - 0.8AB*2x)*0.5}{(Ax - Bx + B + 0.8ABx - 0.8ABx^{2})(Ax - Bx + B + 0.8ABx - 0.8ABx^{2})^{\frac{1}{2}}}\\=&\frac{A}{sqrt(Ax - Bx + B + 0.8ABx - 0.8ABx^{2})} - \frac{0.5A^{2}x}{(Ax - Bx + B + 0.8ABx - 0.8ABx^{2})(Ax - Bx + B + 0.8ABx - 0.8ABx^{2})^{\frac{1}{2}}} + \frac{0.5ABx}{(Ax - Bx + B + 0.8ABx - 0.8ABx^{2})(Ax - Bx + B + 0.8ABx - 0.8ABx^{2})^{\frac{1}{2}}} - \frac{0.4A^{2}Bx}{(Ax - Bx + B + 0.8ABx - 0.8ABx^{2})(Ax - Bx + B + 0.8ABx - 0.8ABx^{2})^{\frac{1}{2}}} + \frac{0.8A^{2}Bx^{2}}{(Ax - Bx + B + 0.8ABx - 0.8ABx^{2})(Ax - Bx + B + 0.8ABx - 0.8ABx^{2})^{\frac{1}{2}}} + \frac{0.8AB^{2}x}{(Ax - Bx + B + 0.8ABx - 0.8ABx^{2})(Ax - Bx + B + 0.8ABx - 0.8ABx^{2})^{\frac{1}{2}}} - \frac{0.5B^{2}x}{(Ax - Bx + B + 0.8ABx - 0.8ABx^{2})(Ax - Bx + B + 0.8ABx - 0.8ABx^{2})^{\frac{1}{2}}} + \frac{0.5ABx}{(Ax - Bx + B + 0.8ABx - 0.8ABx^{2})(Ax - Bx + B + 0.8ABx - 0.8ABx^{2})^{\frac{1}{2}}} + \frac{0.4AB^{2}x}{(Ax - Bx + B + 0.8ABx - 0.8ABx^{2})(Ax - Bx + B + 0.8ABx - 0.8ABx^{2})^{\frac{1}{2}}} - \frac{B}{sqrt(Ax - Bx + B + 0.8ABx - 0.8ABx^{2})} - \frac{0.8AB^{2}x^{2}}{(Ax - Bx + B + 0.8ABx - 0.8ABx^{2})(Ax - Bx + B + 0.8ABx - 0.8ABx^{2})^{\frac{1}{2}}} + \frac{0.5B^{2}}{(Ax - Bx + B + 0.8ABx - 0.8ABx^{2})(Ax - Bx + B + 0.8ABx - 0.8ABx^{2})^{\frac{1}{2}}} - \frac{0.064ABx}{(Ax - Bx + B + 0.8ABx - 0.8ABx^{2})(Ax - Bx + B + 0.8ABx - 0.8ABx^{2})^{\frac{1}{2}}} - \frac{0.4AB^{2}}{(Ax - Bx + B + 0.8ABx - 0.8ABx^{2})(Ax - Bx + B + 0.8ABx - 0.8ABx^{2})^{\frac{1}{2}}} + \frac{0.032AB}{(Ax - Bx + B + 0.8ABx - 0.8ABx^{2})(Ax - Bx + B + 0.8ABx - 0.8ABx^{2})^{\frac{1}{2}}} - \frac{0.04B}{(Ax - Bx + B + 0.8ABx - 0.8ABx^{2})(Ax - Bx + B + 0.8ABx - 0.8ABx^{2})^{\frac{1}{2}}} - \frac{0.5AB}{(Ax - Bx + B + 0.8ABx - 0.8ABx^{2})(Ax - Bx + B + 0.8ABx - 0.8ABx^{2})^{\frac{1}{2}}} + \frac{0.04A}{(Ax - Bx + B + 0.8ABx - 0.8ABx^{2})(Ax - Bx + B + 0.8ABx - 0.8ABx^{2})^{\frac{1}{2}}}\\ \end{split}\end{equation} \]

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