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。
\[ \begin{equation}\begin{split}【1/1】求函数cos(sin(tan(sin(cos({x}^{6} - 100) + {\frac{1}{x}}^{100})))) 关于 x 的 1 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = cos(sin(tan(sin(cos(x^{6} - 100) + \frac{1}{x^{100}}))))\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( cos(sin(tan(sin(cos(x^{6} - 100) + \frac{1}{x^{100}}))))\right)}{dx}\\=&-sin(sin(tan(sin(cos(x^{6} - 100) + \frac{1}{x^{100}}))))cos(tan(sin(cos(x^{6} - 100) + \frac{1}{x^{100}})))sec^{2}(sin(cos(x^{6} - 100) + \frac{1}{x^{100}}))(cos(cos(x^{6} - 100) + \frac{1}{x^{100}})(-sin(x^{6} - 100)(6x^{5} + 0) + \frac{-100}{x^{101}}))\\=&6x^{5}sin(x^{6} - 100)sin(sin(tan(sin(cos(x^{6} - 100) + \frac{1}{x^{100}}))))cos(cos(x^{6} - 100) + \frac{1}{x^{100}})cos(tan(sin(cos(x^{6} - 100) + \frac{1}{x^{100}})))sec^{2}(sin(cos(x^{6} - 100) + \frac{1}{x^{100}})) + \frac{100sin(sin(tan(sin(cos(x^{6} - 100) + \frac{1}{x^{100}}))))cos(cos(x^{6} - 100) + \frac{1}{x^{100}})cos(tan(sin(cos(x^{6} - 100) + \frac{1}{x^{100}})))sec^{2}(sin(cos(x^{6} - 100) + \frac{1}{x^{100}}))}{x^{101}}\\ \end{split}\end{equation} \]

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