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。
\[ \begin{equation}\begin{split}【1/1】求函数ln(x + {(x + 1)}^{\frac{1}{2}}) 关于 x 的 2 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( ln(x + (x + 1)^{\frac{1}{2}})\right)}{dx}\\=&\frac{(1 + ((x + 1)^{\frac{1}{2}}((0)ln(x + 1) + \frac{(\frac{1}{2})(1 + 0)}{(x + 1)})))}{(x + (x + 1)^{\frac{1}{2}})}\\=&\frac{(x + 1)^{\frac{1}{2}}}{2(x + (x + 1)^{\frac{1}{2}})(x + 1)} + \frac{1}{(x + (x + 1)^{\frac{1}{2}})}\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( \frac{(x + 1)^{\frac{1}{2}}}{2(x + (x + 1)^{\frac{1}{2}})(x + 1)} + \frac{1}{(x + (x + 1)^{\frac{1}{2}})}\right)}{dx}\\=&\frac{(\frac{\frac{1}{2}(1 + 0)}{(x + 1)^{\frac{1}{2}}})}{2(x + (x + 1)^{\frac{1}{2}})(x + 1)} + \frac{(x + 1)^{\frac{1}{2}}(\frac{-(1 + (\frac{\frac{1}{2}(1 + 0)}{(x + 1)^{\frac{1}{2}}}))}{(x + (x + 1)^{\frac{1}{2}})^{2}})}{2(x + 1)} + \frac{(x + 1)^{\frac{1}{2}}(\frac{-(1 + 0)}{(x + 1)^{2}})}{2(x + (x + 1)^{\frac{1}{2}})} + (\frac{-(1 + (\frac{\frac{1}{2}(1 + 0)}{(x + 1)^{\frac{1}{2}}}))}{(x + (x + 1)^{\frac{1}{2}})^{2}})\\=&\frac{-1}{4(x + 1)^{\frac{3}{2}}(x + (x + 1)^{\frac{1}{2}})} - \frac{1}{4(x + (x + 1)^{\frac{1}{2}})^{2}(x + 1)} - \frac{1}{(x + (x + 1)^{\frac{1}{2}})^{2}(x + 1)^{\frac{1}{2}}} - \frac{1}{(x + (x + 1)^{\frac{1}{2}})^{2}}\\ \end{split}\end{equation} \]

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