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。
\[ \begin{equation}\begin{split}【1/1】求函数(sin(5x))({(tan({x}^{2}) - x)}^{3}) 关于 x 的 1 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = sin(5x)tan^{3}(x^{2}) - 3xsin(5x)tan^{2}(x^{2}) + 3x^{2}sin(5x)tan(x^{2}) - x^{3}sin(5x)\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( sin(5x)tan^{3}(x^{2}) - 3xsin(5x)tan^{2}(x^{2}) + 3x^{2}sin(5x)tan(x^{2}) - x^{3}sin(5x)\right)}{dx}\\=&cos(5x)*5tan^{3}(x^{2}) + sin(5x)*3tan^{2}(x^{2})sec^{2}(x^{2})(2x) - 3sin(5x)tan^{2}(x^{2}) - 3xcos(5x)*5tan^{2}(x^{2}) - 3xsin(5x)*2tan(x^{2})sec^{2}(x^{2})(2x) + 3*2xsin(5x)tan(x^{2}) + 3x^{2}cos(5x)*5tan(x^{2}) + 3x^{2}sin(5x)sec^{2}(x^{2})(2x) - 3x^{2}sin(5x) - x^{3}cos(5x)*5\\=&5cos(5x)tan^{3}(x^{2}) + 6xsin(5x)tan^{2}(x^{2})sec^{2}(x^{2}) - 3sin(5x)tan^{2}(x^{2}) - 15xcos(5x)tan^{2}(x^{2}) - 12x^{2}sin(5x)tan(x^{2})sec^{2}(x^{2}) + 6xsin(5x)tan(x^{2}) + 15x^{2}cos(5x)tan(x^{2}) + 6x^{3}sin(5x)sec^{2}(x^{2}) - 3x^{2}sin(5x) - 5x^{3}cos(5x)\\ \end{split}\end{equation} \]

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