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。
\[ \begin{equation}\begin{split}【1/1】求函数\frac{-ln(2)}{((1 + x)({ln(1 + x)}^{2}))} 关于 x 的 1 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = \frac{-ln(2)}{(ln^{2}(x + 1) + xln^{2}(x + 1))}\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( \frac{-ln(2)}{(ln^{2}(x + 1) + xln^{2}(x + 1))}\right)}{dx}\\=&-(\frac{-(\frac{2ln(x + 1)(1 + 0)}{(x + 1)} + ln^{2}(x + 1) + \frac{x*2ln(x + 1)(1 + 0)}{(x + 1)})}{(ln^{2}(x + 1) + xln^{2}(x + 1))^{2}})ln(2) - \frac{0}{(ln^{2}(x + 1) + xln^{2}(x + 1))(2)}\\=&\frac{2ln(x + 1)ln(2)}{(ln^{2}(x + 1) + xln^{2}(x + 1))^{2}(x + 1)} + \frac{ln^{2}(x + 1)ln(2)}{(ln^{2}(x + 1) + xln^{2}(x + 1))^{2}} + \frac{2xln(x + 1)ln(2)}{(ln^{2}(x + 1) + xln^{2}(x + 1))^{2}(x + 1)}\\ \end{split}\end{equation} \]

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