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。
\[ \begin{equation}\begin{split}【1/1】求函数{x}^{4}tan(({x}^{3})({e}^{4})){e}^{(({x}^{2}){(sec({x}^{5}))}^{3})} 关于 x 的 1 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = x^{4}{e}^{(x^{2}sec^{3}(x^{5}))}tan(x^{3}e^{4})\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( x^{4}{e}^{(x^{2}sec^{3}(x^{5}))}tan(x^{3}e^{4})\right)}{dx}\\=&4x^{3}{e}^{(x^{2}sec^{3}(x^{5}))}tan(x^{3}e^{4}) + x^{4}({e}^{(x^{2}sec^{3}(x^{5}))}((2xsec^{3}(x^{5}) + x^{2}*3sec^{3}(x^{5})tan(x^{5})*5x^{4})ln(e) + \frac{(x^{2}sec^{3}(x^{5}))(0)}{(e)}))tan(x^{3}e^{4}) + x^{4}{e}^{(x^{2}sec^{3}(x^{5}))}sec^{2}(x^{3}e^{4})(3x^{2}e^{4} + x^{3}*4e^{3}*0)\\=&2x^{5}{e}^{(x^{2}sec^{3}(x^{5}))}tan(x^{3}e^{4})sec^{3}(x^{5}) + 15x^{10}{e}^{(x^{2}sec^{3}(x^{5}))}tan(x^{5})tan(x^{3}e^{4})sec^{3}(x^{5}) + 4x^{3}{e}^{(x^{2}sec^{3}(x^{5}))}tan(x^{3}e^{4}) + 3x^{6}{e}^{(x^{2}sec^{3}(x^{5}))}e^{4}sec^{2}(x^{3}e^{4})\\ \end{split}\end{equation} \]

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