本次共计算 1 个题目：每一题对 x 求 3 阶导数。
    注意，变量是区分大小写的。
$$\begin{equation}\begin{split}【1/1】求函数{(th({x}^{3}))}^{5} 关于 x 的 3 阶导数：\\\end{split}\end{equation}$$ $$\begin{equation}\begin{split}\\解:&\\ &原函数 = th^{5}(x^{3})\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( th^{5}(x^{3})\right)}{dx}\\=&5th^{4}(x^{3})(1 - th^{2}(x^{3}))*3x^{2}\\=&15x^{2}th^{4}(x^{3}) - 15x^{2}th^{6}(x^{3})\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( 15x^{2}th^{4}(x^{3}) - 15x^{2}th^{6}(x^{3})\right)}{dx}\\=&15*2xth^{4}(x^{3}) + 15x^{2}*4th^{3}(x^{3})(1 - th^{2}(x^{3}))*3x^{2} - 15*2xth^{6}(x^{3}) - 15x^{2}*6th^{5}(x^{3})(1 - th^{2}(x^{3}))*3x^{2}\\=&30xth^{4}(x^{3}) + 180x^{4}th^{3}(x^{3}) - 450x^{4}th^{5}(x^{3}) - 30xth^{6}(x^{3}) + 270x^{4}th^{7}(x^{3})\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( 30xth^{4}(x^{3}) + 180x^{4}th^{3}(x^{3}) - 450x^{4}th^{5}(x^{3}) - 30xth^{6}(x^{3}) + 270x^{4}th^{7}(x^{3})\right)}{dx}\\=&30th^{4}(x^{3}) + 30x*4th^{3}(x^{3})(1 - th^{2}(x^{3}))*3x^{2} + 180*4x^{3}th^{3}(x^{3}) + 180x^{4}*3th^{2}(x^{3})(1 - th^{2}(x^{3}))*3x^{2} - 450*4x^{3}th^{5}(x^{3}) - 450x^{4}*5th^{4}(x^{3})(1 - th^{2}(x^{3}))*3x^{2} - 30th^{6}(x^{3}) - 30x*6th^{5}(x^{3})(1 - th^{2}(x^{3}))*3x^{2} + 270*4x^{3}th^{7}(x^{3}) + 270x^{4}*7th^{6}(x^{3})(1 - th^{2}(x^{3}))*3x^{2}\\=&30th^{4}(x^{3}) + 1080x^{3}th^{3}(x^{3}) - 2700x^{3}th^{5}(x^{3}) + 1620x^{6}th^{2}(x^{3}) - 8370x^{6}th^{4}(x^{3}) + 12420x^{6}th^{6}(x^{3}) - 30th^{6}(x^{3}) + 1620x^{3}th^{7}(x^{3}) - 5670x^{6}th^{8}(x^{3})\\ \end{split}\end{equation}$$

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