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。
\[ \begin{equation}\begin{split}【1/1】求函数ln({x}^{2}sin(x) + ln(x)) + sin(x)cos(x)tan(x) - lg(x)e 关于 x 的 1 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = ln(x^{2}sin(x) + ln(x)) + sin(x)cos(x)tan(x) - elg(x)\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( ln(x^{2}sin(x) + ln(x)) + sin(x)cos(x)tan(x) - elg(x)\right)}{dx}\\=&\frac{(2xsin(x) + x^{2}cos(x) + \frac{1}{(x)})}{(x^{2}sin(x) + ln(x))} + cos(x)cos(x)tan(x) + sin(x)*-sin(x)tan(x) + sin(x)cos(x)sec^{2}(x)(1) - 0lg(x) - \frac{e}{ln{10}(x)}\\=&\frac{2xsin(x)}{(x^{2}sin(x) + ln(x))} + \frac{x^{2}cos(x)}{(x^{2}sin(x) + ln(x))} + \frac{1}{(x^{2}sin(x) + ln(x))x} + cos^{2}(x)tan(x) - sin^{2}(x)tan(x) + sin(x)cos(x)sec^{2}(x) - \frac{e}{xln{10}}\\ \end{split}\end{equation} \]

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