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。
\[ \begin{equation}\begin{split}【1/1】求函数\frac{(1 + e^{-3}){(1 - x)}^{4}log_{2}^{x}}{(e^{-3} + {(1 - x)}^{5})} 关于 x 的 1 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = \frac{x^{4}log_{2}^{x}e^{-3}}{(e^{-3} - x^{5} + 5x^{4} - 10x^{3} + 10x^{2} - 5x + 1)} - \frac{4x^{3}log_{2}^{x}e^{-3}}{(e^{-3} - x^{5} + 5x^{4} - 10x^{3} + 10x^{2} - 5x + 1)} + \frac{6x^{2}log_{2}^{x}e^{-3}}{(e^{-3} - x^{5} + 5x^{4} - 10x^{3} + 10x^{2} - 5x + 1)} - \frac{4xlog_{2}^{x}e^{-3}}{(e^{-3} - x^{5} + 5x^{4} - 10x^{3} + 10x^{2} - 5x + 1)} + \frac{log_{2}^{x}e^{-3}}{(e^{-3} - x^{5} + 5x^{4} - 10x^{3} + 10x^{2} - 5x + 1)} + \frac{x^{4}log_{2}^{x}}{(e^{-3} - x^{5} + 5x^{4} - 10x^{3} + 10x^{2} - 5x + 1)} - \frac{4x^{3}log_{2}^{x}}{(e^{-3} - x^{5} + 5x^{4} - 10x^{3} + 10x^{2} - 5x + 1)} + \frac{6x^{2}log_{2}^{x}}{(e^{-3} - x^{5} + 5x^{4} - 10x^{3} + 10x^{2} - 5x + 1)} - \frac{4xlog_{2}^{x}}{(e^{-3} - x^{5} + 5x^{4} - 10x^{3} + 10x^{2} - 5x + 1)} + \frac{log_{2}^{x}}{(e^{-3} - x^{5} + 5x^{4} - 10x^{3} + 10x^{2} - 5x + 1)}\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( \frac{x^{4}log_{2}^{x}e^{-3}}{(e^{-3} - x^{5} + 5x^{4} - 10x^{3} + 10x^{2} - 5x + 1)} - \frac{4x^{3}log_{2}^{x}e^{-3}}{(e^{-3} - x^{5} + 5x^{4} - 10x^{3} + 10x^{2} - 5x + 1)} + \frac{6x^{2}log_{2}^{x}e^{-3}}{(e^{-3} - x^{5} + 5x^{4} - 10x^{3} + 10x^{2} - 5x + 1)} - \frac{4xlog_{2}^{x}e^{-3}}{(e^{-3} - x^{5} + 5x^{4} - 10x^{3} + 10x^{2} - 5x + 1)} + \frac{log_{2}^{x}e^{-3}}{(e^{-3} - x^{5} + 5x^{4} - 10x^{3} + 10x^{2} - 5x + 1)} + \frac{x^{4}log_{2}^{x}}{(e^{-3} - x^{5} + 5x^{4} - 10x^{3} + 10x^{2} - 5x + 1)} - \frac{4x^{3}log_{2}^{x}}{(e^{-3} - x^{5} + 5x^{4} - 10x^{3} + 10x^{2} - 5x + 1)} + \frac{6x^{2}log_{2}^{x}}{(e^{-3} - x^{5} + 5x^{4} - 10x^{3} + 10x^{2} - 5x + 1)} - \frac{4xlog_{2}^{x}}{(e^{-3} - x^{5} + 5x^{4} - 10x^{3} + 10x^{2} - 5x + 1)} + \frac{log_{2}^{x}}{(e^{-3} - x^{5} + 5x^{4} - 10x^{3} + 10x^{2} - 5x + 1)}\right)}{dx}\\=&(\frac{-(e^{-3}*0 - 5x^{4} + 5*4x^{3} - 10*3x^{2} + 10*2x - 5 + 0)}{(e^{-3} - x^{5} + 5x^{4} - 10x^{3} + 10x^{2} - 5x + 1)^{2}})x^{4}log_{2}^{x}e^{-3} + \frac{4x^{3}log_{2}^{x}e^{-3}}{(e^{-3} - x^{5} + 5x^{4} - 10x^{3} + 10x^{2} - 5x + 1)} + \frac{x^{4}(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{2}^{x}}{(2)})}{(ln(2))})e^{-3}}{(e^{-3} - x^{5} + 5x^{4} - 10x^{3} + 10x^{2} - 5x + 1)} + \frac{x^{4}log_{2}^{x}e^{-3}*0}{(e^{-3} - x^{5} + 5x^{4} - 10x^{3} + 10x^{2} - 5x + 1)} - 4(\frac{-(e^{-3}*0 - 5x^{4} + 5*4x^{3} - 10*3x^{2} + 10*2x - 5 + 0)}{(e^{-3} - x^{5} + 5x^{4} - 10x^{3} + 10x^{2} - 5x + 1)^{2}})x^{3}log_{2}^{x}e^{-3} - \frac{4*3x^{2}log_{2}^{x}e^{-3}}{(e^{-3} - x^{5} + 5x^{4} - 10x^{3} + 10x^{2} - 5x + 1)} - \frac{4x^{3}(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{2}^{x}}{(2)})}{(ln(2))})e^{-3}}{(e^{-3} - x^{5} + 5x^{4} - 10x^{3} + 10x^{2} - 5x + 1)} - \frac{4x^{3}log_{2}^{x}e^{-3}*0}{(e^{-3} - x^{5} + 5x^{4} - 10x^{3} + 10x^{2} - 5x + 1)} + 6(\frac{-(e^{-3}*0 - 5x^{4} + 5*4x^{3} - 10*3x^{2} + 10*2x - 5 + 0)}{(e^{-3} - x^{5} + 5x^{4} - 10x^{3} + 10x^{2} - 5x + 1)^{2}})x^{2}log_{2}^{x}e^{-3} + \frac{6*2xlog_{2}^{x}e^{-3}}{(e^{-3} - x^{5} + 5x^{4} - 10x^{3} + 10x^{2} - 5x + 1)} + \frac{6x^{2}(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{2}^{x}}{(2)})}{(ln(2))})e^{-3}}{(e^{-3} - x^{5} + 5x^{4} - 10x^{3} + 10x^{2} - 5x + 1)} + \frac{6x^{2}log_{2}^{x}e^{-3}*0}{(e^{-3} - x^{5} + 5x^{4} - 10x^{3} + 10x^{2} - 5x + 1)} - 4(\frac{-(e^{-3}*0 - 5x^{4} + 5*4x^{3} - 10*3x^{2} + 10*2x - 5 + 0)}{(e^{-3} - x^{5} + 5x^{4} - 10x^{3} + 10x^{2} - 5x + 1)^{2}})xlog_{2}^{x}e^{-3} - \frac{4log_{2}^{x}e^{-3}}{(e^{-3} - x^{5} + 5x^{4} - 10x^{3} + 10x^{2} - 5x + 1)} - \frac{4x(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{2}^{x}}{(2)})}{(ln(2))})e^{-3}}{(e^{-3} - x^{5} + 5x^{4} - 10x^{3} + 10x^{2} - 5x + 1)} - \frac{4xlog_{2}^{x}e^{-3}*0}{(e^{-3} - x^{5} + 5x^{4} - 10x^{3} + 10x^{2} - 5x + 1)} + (\frac{-(e^{-3}*0 - 5x^{4} + 5*4x^{3} - 10*3x^{2} + 10*2x - 5 + 0)}{(e^{-3} - x^{5} + 5x^{4} - 10x^{3} + 10x^{2} - 5x + 1)^{2}})log_{2}^{x}e^{-3} + \frac{(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{2}^{x}}{(2)})}{(ln(2))})e^{-3}}{(e^{-3} - x^{5} + 5x^{4} - 10x^{3} + 10x^{2} - 5x + 1)} + \frac{log_{2}^{x}e^{-3}*0}{(e^{-3} - x^{5} + 5x^{4} - 10x^{3} + 10x^{2} - 5x + 1)} + (\frac{-(e^{-3}*0 - 5x^{4} + 5*4x^{3} - 10*3x^{2} + 10*2x - 5 + 0)}{(e^{-3} - x^{5} + 5x^{4} - 10x^{3} + 10x^{2} - 5x + 1)^{2}})x^{4}log_{2}^{x} + \frac{4x^{3}log_{2}^{x}}{(e^{-3} - x^{5} + 5x^{4} - 10x^{3} + 10x^{2} - 5x + 1)} + \frac{x^{4}(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{2}^{x}}{(2)})}{(ln(2))})}{(e^{-3} - x^{5} + 5x^{4} - 10x^{3} + 10x^{2} - 5x + 1)} - 4(\frac{-(e^{-3}*0 - 5x^{4} + 5*4x^{3} - 10*3x^{2} + 10*2x - 5 + 0)}{(e^{-3} - x^{5} + 5x^{4} - 10x^{3} + 10x^{2} - 5x + 1)^{2}})x^{3}log_{2}^{x} - \frac{4*3x^{2}log_{2}^{x}}{(e^{-3} - x^{5} + 5x^{4} - 10x^{3} + 10x^{2} - 5x + 1)} - \frac{4x^{3}(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{2}^{x}}{(2)})}{(ln(2))})}{(e^{-3} - x^{5} + 5x^{4} - 10x^{3} + 10x^{2} - 5x + 1)} + 6(\frac{-(e^{-3}*0 - 5x^{4} + 5*4x^{3} - 10*3x^{2} + 10*2x - 5 + 0)}{(e^{-3} - x^{5} + 5x^{4} - 10x^{3} + 10x^{2} - 5x + 1)^{2}})x^{2}log_{2}^{x} + \frac{6*2xlog_{2}^{x}}{(e^{-3} - x^{5} + 5x^{4} - 10x^{3} + 10x^{2} - 5x + 1)} + \frac{6x^{2}(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{2}^{x}}{(2)})}{(ln(2))})}{(e^{-3} - x^{5} + 5x^{4} - 10x^{3} + 10x^{2} - 5x + 1)} - 4(\frac{-(e^{-3}*0 - 5x^{4} + 5*4x^{3} - 10*3x^{2} + 10*2x - 5 + 0)}{(e^{-3} - x^{5} + 5x^{4} - 10x^{3} + 10x^{2} - 5x + 1)^{2}})xlog_{2}^{x} - \frac{4log_{2}^{x}}{(e^{-3} - x^{5} + 5x^{4} - 10x^{3} + 10x^{2} - 5x + 1)} - \frac{4x(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{2}^{x}}{(2)})}{(ln(2))})}{(e^{-3} - x^{5} + 5x^{4} - 10x^{3} + 10x^{2} - 5x + 1)} + (\frac{-(e^{-3}*0 - 5x^{4} + 5*4x^{3} - 10*3x^{2} + 10*2x - 5 + 0)}{(e^{-3} - x^{5} + 5x^{4} - 10x^{3} + 10x^{2} - 5x + 1)^{2}})log_{2}^{x} + \frac{(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{2}^{x}}{(2)})}{(ln(2))})}{(e^{-3} - x^{5} + 5x^{4} - 10x^{3} + 10x^{2} - 5x + 1)}\\=&\frac{5x^{8}log_{2}^{x}e^{-3}}{(e^{-3} - x^{5} + 5x^{4} - 10x^{3} + 10x^{2} - 5x + 1)^{2}} - \frac{40x^{7}log_{2}^{x}e^{-3}}{(e^{-3} - x^{5} + 5x^{4} - 10x^{3} + 10x^{2} - 5x + 1)^{2}} + \frac{140x^{6}log_{2}^{x}e^{-3}}{(e^{-3} - x^{5} + 5x^{4} - 10x^{3} + 10x^{2} - 5x + 1)^{2}} - \frac{280x^{5}log_{2}^{x}e^{-3}}{(e^{-3} - x^{5} + 5x^{4} - 10x^{3} + 10x^{2} - 5x + 1)^{2}} + \frac{4x^{3}log_{2}^{x}e^{-3}}{(e^{-3} - x^{5} + 5x^{4} - 10x^{3} + 10x^{2} - 5x + 1)} + \frac{x^{3}e^{-3}}{(e^{-3} - x^{5} + 5x^{4} - 10x^{3} + 10x^{2} - 5x + 1)ln(2)} + \frac{350x^{4}log_{2}^{x}e^{-3}}{(e^{-3} - x^{5} + 5x^{4} - 10x^{3} + 10x^{2} - 5x + 1)^{2}} - \frac{12x^{2}log_{2}^{x}e^{-3}}{(e^{-3} - x^{5} + 5x^{4} - 10x^{3} + 10x^{2} - 5x + 1)} - \frac{4x^{2}e^{-3}}{(e^{-3} - x^{5} + 5x^{4} - 10x^{3} + 10x^{2} - 5x + 1)ln(2)} - \frac{280x^{3}log_{2}^{x}e^{-3}}{(e^{-3} - x^{5} + 5x^{4} - 10x^{3} + 10x^{2} - 5x + 1)^{2}} + \frac{140x^{2}log_{2}^{x}e^{-3}}{(e^{-3} - x^{5} + 5x^{4} - 10x^{3} + 10x^{2} - 5x + 1)^{2}} + \frac{12xlog_{2}^{x}e^{-3}}{(e^{-3} - x^{5} + 5x^{4} - 10x^{3} + 10x^{2} - 5x + 1)} + \frac{6xe^{-3}}{(e^{-3} - x^{5} + 5x^{4} - 10x^{3} + 10x^{2} - 5x + 1)ln(2)} - \frac{40xlog_{2}^{x}e^{-3}}{(e^{-3} - x^{5} + 5x^{4} - 10x^{3} + 10x^{2} - 5x + 1)^{2}} - \frac{4log_{2}^{x}e^{-3}}{(e^{-3} - x^{5} + 5x^{4} - 10x^{3} + 10x^{2} - 5x + 1)} - \frac{4e^{-3}}{(e^{-3} - x^{5} + 5x^{4} - 10x^{3} + 10x^{2} - 5x + 1)ln(2)} + \frac{5log_{2}^{x}e^{-3}}{(e^{-3} - x^{5} + 5x^{4} - 10x^{3} + 10x^{2} - 5x + 1)^{2}} + \frac{e^{-3}}{(e^{-3} - x^{5} + 5x^{4} - 10x^{3} + 10x^{2} - 5x + 1)xln(2)} + \frac{5x^{8}log_{2}^{x}}{(e^{-3} - x^{5} + 5x^{4} - 10x^{3} + 10x^{2} - 5x + 1)^{2}} - \frac{40x^{7}log_{2}^{x}}{(e^{-3} - x^{5} + 5x^{4} - 10x^{3} + 10x^{2} - 5x + 1)^{2}} + \frac{140x^{6}log_{2}^{x}}{(e^{-3} - x^{5} + 5x^{4} - 10x^{3} + 10x^{2} - 5x + 1)^{2}} - \frac{280x^{5}log_{2}^{x}}{(e^{-3} - x^{5} + 5x^{4} - 10x^{3} + 10x^{2} - 5x + 1)^{2}} + \frac{4x^{3}log_{2}^{x}}{(e^{-3} - x^{5} + 5x^{4} - 10x^{3} + 10x^{2} - 5x + 1)} + \frac{x^{3}}{(e^{-3} - x^{5} + 5x^{4} - 10x^{3} + 10x^{2} - 5x + 1)ln(2)} + \frac{350x^{4}log_{2}^{x}}{(e^{-3} - x^{5} + 5x^{4} - 10x^{3} + 10x^{2} - 5x + 1)^{2}} - \frac{12x^{2}log_{2}^{x}}{(e^{-3} - x^{5} + 5x^{4} - 10x^{3} + 10x^{2} - 5x + 1)} - \frac{4x^{2}}{(e^{-3} - x^{5} + 5x^{4} - 10x^{3} + 10x^{2} - 5x + 1)ln(2)} - \frac{280x^{3}log_{2}^{x}}{(e^{-3} - x^{5} + 5x^{4} - 10x^{3} + 10x^{2} - 5x + 1)^{2}} + \frac{140x^{2}log_{2}^{x}}{(e^{-3} - x^{5} + 5x^{4} - 10x^{3} + 10x^{2} - 5x + 1)^{2}} + \frac{12xlog_{2}^{x}}{(e^{-3} - x^{5} + 5x^{4} - 10x^{3} + 10x^{2} - 5x + 1)} + \frac{6x}{(e^{-3} - x^{5} + 5x^{4} - 10x^{3} + 10x^{2} - 5x + 1)ln(2)} - \frac{40xlog_{2}^{x}}{(e^{-3} - x^{5} + 5x^{4} - 10x^{3} + 10x^{2} - 5x + 1)^{2}} - \frac{4log_{2}^{x}}{(e^{-3} - x^{5} + 5x^{4} - 10x^{3} + 10x^{2} - 5x + 1)} - \frac{4}{(e^{-3} - x^{5} + 5x^{4} - 10x^{3} + 10x^{2} - 5x + 1)ln(2)} + \frac{5log_{2}^{x}}{(e^{-3} - x^{5} + 5x^{4} - 10x^{3} + 10x^{2} - 5x + 1)^{2}} + \frac{1}{(e^{-3} - x^{5} + 5x^{4} - 10x^{3} + 10x^{2} - 5x + 1)xln(2)}\\ \end{split}\end{equation} \]

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