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。
\[ \begin{equation}\begin{split}【1/1】求函数\frac{(2ln(x) + {x}^{3})}{(3ln(x) + {x}^{2})} 关于 x 的 1 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = \frac{2ln(x)}{(3ln(x) + x^{2})} + \frac{x^{3}}{(3ln(x) + x^{2})}\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( \frac{2ln(x)}{(3ln(x) + x^{2})} + \frac{x^{3}}{(3ln(x) + x^{2})}\right)}{dx}\\=&2(\frac{-(\frac{3}{(x)} + 2x)}{(3ln(x) + x^{2})^{2}})ln(x) + \frac{2}{(3ln(x) + x^{2})(x)} + (\frac{-(\frac{3}{(x)} + 2x)}{(3ln(x) + x^{2})^{2}})x^{3} + \frac{3x^{2}}{(3ln(x) + x^{2})}\\=&\frac{-6ln(x)}{(3ln(x) + x^{2})^{2}x} - \frac{4xln(x)}{(3ln(x) + x^{2})^{2}} + \frac{2}{(3ln(x) + x^{2})x} - \frac{3x^{2}}{(3ln(x) + x^{2})^{2}} - \frac{2x^{4}}{(3ln(x) + x^{2})^{2}} + \frac{3x^{2}}{(3ln(x) + x^{2})}\\ \end{split}\end{equation} \]

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