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。
\[ \begin{equation}\begin{split}【1/1】求函数sec(x{\frac{1}{5}}^{x}){(cos(x{\frac{1}{5}}^{x}))}^{2} 关于 x 的 1 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = cos^{2}(x{\frac{1}{5}}^{x})sec(x{\frac{1}{5}}^{x})\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( cos^{2}(x{\frac{1}{5}}^{x})sec(x{\frac{1}{5}}^{x})\right)}{dx}\\=&-2cos(x{\frac{1}{5}}^{x})sin(x{\frac{1}{5}}^{x})({\frac{1}{5}}^{x} + x({\frac{1}{5}}^{x}((1)ln(\frac{1}{5}) + \frac{(x)(0)}{(\frac{1}{5})})))sec(x{\frac{1}{5}}^{x}) + cos^{2}(x{\frac{1}{5}}^{x})sec(x{\frac{1}{5}}^{x})tan(x{\frac{1}{5}}^{x})({\frac{1}{5}}^{x} + x({\frac{1}{5}}^{x}((1)ln(\frac{1}{5}) + \frac{(x)(0)}{(\frac{1}{5})})))\\=&-2 * {\frac{1}{5}}^{x}sin(x{\frac{1}{5}}^{x})cos(x{\frac{1}{5}}^{x})sec(x{\frac{1}{5}}^{x}) - 2x{\frac{1}{5}}^{x}ln(\frac{1}{5})sin(x{\frac{1}{5}}^{x})cos(x{\frac{1}{5}}^{x})sec(x{\frac{1}{5}}^{x}) + {\frac{1}{5}}^{x}cos^{2}(x{\frac{1}{5}}^{x})tan(x{\frac{1}{5}}^{x})sec(x{\frac{1}{5}}^{x}) + x{\frac{1}{5}}^{x}ln(\frac{1}{5})cos^{2}(x{\frac{1}{5}}^{x})tan(x{\frac{1}{5}}^{x})sec(x{\frac{1}{5}}^{x})\\ \end{split}\end{equation} \]

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