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

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