本次共计算 1 个题目：每一题对 x 求 4 阶导数。
    注意，变量是区分大小写的。
\[ \begin{equation}\begin{split}【1/1】求函数{e}^{{x}^{3}} 关于 x 的 4 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = {e}^{x^{3}}\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( {e}^{x^{3}}\right)}{dx}\\=&({e}^{x^{3}}((3x^{2})ln(e) + \frac{(x^{3})(0)}{(e)}))\\=&3x^{2}{e}^{x^{3}}\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( 3x^{2}{e}^{x^{3}}\right)}{dx}\\=&3*2x{e}^{x^{3}} + 3x^{2}({e}^{x^{3}}((3x^{2})ln(e) + \frac{(x^{3})(0)}{(e)}))\\=&6x{e}^{x^{3}} + 9x^{4}{e}^{x^{3}}\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( 6x{e}^{x^{3}} + 9x^{4}{e}^{x^{3}}\right)}{dx}\\=&6{e}^{x^{3}} + 6x({e}^{x^{3}}((3x^{2})ln(e) + \frac{(x^{3})(0)}{(e)})) + 9*4x^{3}{e}^{x^{3}} + 9x^{4}({e}^{x^{3}}((3x^{2})ln(e) + \frac{(x^{3})(0)}{(e)}))\\=&6{e}^{x^{3}} + 54x^{3}{e}^{x^{3}} + 27x^{6}{e}^{x^{3}}\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( 6{e}^{x^{3}} + 54x^{3}{e}^{x^{3}} + 27x^{6}{e}^{x^{3}}\right)}{dx}\\=&6({e}^{x^{3}}((3x^{2})ln(e) + \frac{(x^{3})(0)}{(e)})) + 54*3x^{2}{e}^{x^{3}} + 54x^{3}({e}^{x^{3}}((3x^{2})ln(e) + \frac{(x^{3})(0)}{(e)})) + 27*6x^{5}{e}^{x^{3}} + 27x^{6}({e}^{x^{3}}((3x^{2})ln(e) + \frac{(x^{3})(0)}{(e)}))\\=&180x^{2}{e}^{x^{3}} + 324x^{5}{e}^{x^{3}} + 81x^{8}{e}^{x^{3}}\\ \end{split}\end{equation} \]

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