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

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