求导函数：
输入一个原函数（即需要求导的函数），然后设置需要求导的变量和求导的阶数，点击“下一步”按钮，即可获得该函数相应阶数的导函数。
注意，输入的函数支持数学函数和其它常量。
输入一个原函数（即需要求导的函数），然后设置需要求导的变量和求导的阶数，点击“下一步”按钮，即可获得该函数相应阶数的导函数。
注意，输入的函数支持数学函数和其它常量。
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。
\[ \begin{equation}\begin{split}【1/1】求函数e^{6{x}^{3} - 6(2a + 1){x}^{2} + 12ax + 16{a}^{2}} 关于 x 的 4 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}}\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}}\right)}{dx}\\=&e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}}(6*3x^{2} - 12a*2x - 6*2x + 12a + 0)\\=&18x^{2}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} - 24axe^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} - 12xe^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} + 12ae^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}}\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( 18x^{2}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} - 24axe^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} - 12xe^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} + 12ae^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}}\right)}{dx}\\=&18*2xe^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} + 18x^{2}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}}(6*3x^{2} - 12a*2x - 6*2x + 12a + 0) - 24ae^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} - 24axe^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}}(6*3x^{2} - 12a*2x - 6*2x + 12a + 0) - 12e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} - 12xe^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}}(6*3x^{2} - 12a*2x - 6*2x + 12a + 0) + 12ae^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}}(6*3x^{2} - 12a*2x - 6*2x + 12a + 0)\\=&36xe^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} + 324x^{4}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} - 864ax^{3}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} - 432x^{3}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} + 1008ax^{2}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} - 24ae^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} + 576a^{2}x^{2}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} - 576a^{2}xe^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} - 12e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} + 144x^{2}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} - 288axe^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} + 144a^{2}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}}\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( 36xe^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} + 324x^{4}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} - 864ax^{3}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} - 432x^{3}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} + 1008ax^{2}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} - 24ae^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} + 576a^{2}x^{2}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} - 576a^{2}xe^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} - 12e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} + 144x^{2}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} - 288axe^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} + 144a^{2}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}}\right)}{dx}\\=&36e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} + 36xe^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}}(6*3x^{2} - 12a*2x - 6*2x + 12a + 0) + 324*4x^{3}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} + 324x^{4}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}}(6*3x^{2} - 12a*2x - 6*2x + 12a + 0) - 864a*3x^{2}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} - 864ax^{3}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}}(6*3x^{2} - 12a*2x - 6*2x + 12a + 0) - 432*3x^{2}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} - 432x^{3}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}}(6*3x^{2} - 12a*2x - 6*2x + 12a + 0) + 1008a*2xe^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} + 1008ax^{2}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}}(6*3x^{2} - 12a*2x - 6*2x + 12a + 0) - 24ae^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}}(6*3x^{2} - 12a*2x - 6*2x + 12a + 0) + 576a^{2}*2xe^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} + 576a^{2}x^{2}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}}(6*3x^{2} - 12a*2x - 6*2x + 12a + 0) - 576a^{2}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} - 576a^{2}xe^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}}(6*3x^{2} - 12a*2x - 6*2x + 12a + 0) - 12e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}}(6*3x^{2} - 12a*2x - 6*2x + 12a + 0) + 144*2xe^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} + 144x^{2}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}}(6*3x^{2} - 12a*2x - 6*2x + 12a + 0) - 288ae^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} - 288axe^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}}(6*3x^{2} - 12a*2x - 6*2x + 12a + 0) + 144a^{2}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}}(6*3x^{2} - 12a*2x - 6*2x + 12a + 0)\\=&36e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} + 216x^{3}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} + 1296ax^{2}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} - 1944x^{2}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} + 3024axe^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} + 5832x^{6}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} - 23328ax^{5}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} - 11664x^{5}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} + 42768ax^{4}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} + 31104a^{2}x^{4}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} - 51840a^{2}x^{3}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} + 7776x^{4}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} - 25920ax^{3}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} + 28512a^{2}x^{2}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} - 3456a^{2}xe^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} - 864a^{2}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} - 13824a^{3}x^{3}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} + 20736a^{3}x^{2}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} - 10368a^{3}xe^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} + 432xe^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} - 432ae^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} + 1728a^{3}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}}\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( 36e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} + 216x^{3}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} + 1296ax^{2}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} - 1944x^{2}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} + 3024axe^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} + 5832x^{6}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} - 23328ax^{5}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} - 11664x^{5}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} + 42768ax^{4}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} + 31104a^{2}x^{4}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} - 51840a^{2}x^{3}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} + 7776x^{4}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} - 25920ax^{3}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} + 28512a^{2}x^{2}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} - 3456a^{2}xe^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} - 864a^{2}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} - 13824a^{3}x^{3}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} + 20736a^{3}x^{2}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} - 10368a^{3}xe^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} + 432xe^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} - 432ae^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} + 1728a^{3}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}}\right)}{dx}\\=&36e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}}(6*3x^{2} - 12a*2x - 6*2x + 12a + 0) + 216*3x^{2}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} + 216x^{3}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}}(6*3x^{2} - 12a*2x - 6*2x + 12a + 0) + 1296a*2xe^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} + 1296ax^{2}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}}(6*3x^{2} - 12a*2x - 6*2x + 12a + 0) - 1944*2xe^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} - 1944x^{2}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}}(6*3x^{2} - 12a*2x - 6*2x + 12a + 0) + 3024ae^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} + 3024axe^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}}(6*3x^{2} - 12a*2x - 6*2x + 12a + 0) + 5832*6x^{5}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} + 5832x^{6}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}}(6*3x^{2} - 12a*2x - 6*2x + 12a + 0) - 23328a*5x^{4}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} - 23328ax^{5}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}}(6*3x^{2} - 12a*2x - 6*2x + 12a + 0) - 11664*5x^{4}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} - 11664x^{5}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}}(6*3x^{2} - 12a*2x - 6*2x + 12a + 0) + 42768a*4x^{3}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} + 42768ax^{4}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}}(6*3x^{2} - 12a*2x - 6*2x + 12a + 0) + 31104a^{2}*4x^{3}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} + 31104a^{2}x^{4}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}}(6*3x^{2} - 12a*2x - 6*2x + 12a + 0) - 51840a^{2}*3x^{2}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} - 51840a^{2}x^{3}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}}(6*3x^{2} - 12a*2x - 6*2x + 12a + 0) + 7776*4x^{3}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} + 7776x^{4}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}}(6*3x^{2} - 12a*2x - 6*2x + 12a + 0) - 25920a*3x^{2}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} - 25920ax^{3}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}}(6*3x^{2} - 12a*2x - 6*2x + 12a + 0) + 28512a^{2}*2xe^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} + 28512a^{2}x^{2}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}}(6*3x^{2} - 12a*2x - 6*2x + 12a + 0) - 3456a^{2}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} - 3456a^{2}xe^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}}(6*3x^{2} - 12a*2x - 6*2x + 12a + 0) - 864a^{2}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}}(6*3x^{2} - 12a*2x - 6*2x + 12a + 0) - 13824a^{3}*3x^{2}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} - 13824a^{3}x^{3}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}}(6*3x^{2} - 12a*2x - 6*2x + 12a + 0) + 20736a^{3}*2xe^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} + 20736a^{3}x^{2}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}}(6*3x^{2} - 12a*2x - 6*2x + 12a + 0) - 10368a^{3}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} - 10368a^{3}xe^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}}(6*3x^{2} - 12a*2x - 6*2x + 12a + 0) + 432e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} + 432xe^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}}(6*3x^{2} - 12a*2x - 6*2x + 12a + 0) - 432ae^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}}(6*3x^{2} - 12a*2x - 6*2x + 12a + 0) + 1728a^{3}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}}(6*3x^{2} - 12a*2x - 6*2x + 12a + 0)\\=&-3888x^{2}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} + 12096axe^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} - 4320xe^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} + 3456ae^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} - 54432x^{5}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} + 305856ax^{4}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} - 95904x^{4}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} + 259200ax^{3}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} - 622080a^{2}x^{3}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} - 186624a^{2}x^{2}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} + 62208x^{3}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} - 155520ax^{2}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} + 114048a^{2}xe^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} + 104976x^{8}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} - 559872ax^{7}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} - 279936x^{7}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} + 1399680ax^{6}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} + 1119744a^{2}x^{6}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} - 2612736a^{2}x^{5}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} + 279936x^{6}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} - 1306368ax^{5}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} + 2270592a^{2}x^{4}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} - 995328a^{3}x^{5}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} + 2156544a^{3}x^{4}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} - 1741824a^{3}x^{3}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} + 539136a^{3}x^{2}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} - 8640a^{2}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} - 20736a^{3}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} + 331776a^{4}x^{4}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} - 663552a^{4}x^{3}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} + 497664a^{4}x^{2}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} - 165888a^{4}xe^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} + 432e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} + 20736a^{4}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}}\\ \end{split}\end{equation} \]
注意，变量是区分大小写的。
\[ \begin{equation}\begin{split}【1/1】求函数e^{6{x}^{3} - 6(2a + 1){x}^{2} + 12ax + 16{a}^{2}} 关于 x 的 4 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}}\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}}\right)}{dx}\\=&e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}}(6*3x^{2} - 12a*2x - 6*2x + 12a + 0)\\=&18x^{2}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} - 24axe^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} - 12xe^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} + 12ae^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}}\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( 18x^{2}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} - 24axe^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} - 12xe^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} + 12ae^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}}\right)}{dx}\\=&18*2xe^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} + 18x^{2}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}}(6*3x^{2} - 12a*2x - 6*2x + 12a + 0) - 24ae^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} - 24axe^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}}(6*3x^{2} - 12a*2x - 6*2x + 12a + 0) - 12e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} - 12xe^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}}(6*3x^{2} - 12a*2x - 6*2x + 12a + 0) + 12ae^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}}(6*3x^{2} - 12a*2x - 6*2x + 12a + 0)\\=&36xe^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} + 324x^{4}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} - 864ax^{3}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} - 432x^{3}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} + 1008ax^{2}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} - 24ae^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} + 576a^{2}x^{2}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} - 576a^{2}xe^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} - 12e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} + 144x^{2}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} - 288axe^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} + 144a^{2}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}}\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( 36xe^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} + 324x^{4}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} - 864ax^{3}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} - 432x^{3}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} + 1008ax^{2}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} - 24ae^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} + 576a^{2}x^{2}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} - 576a^{2}xe^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} - 12e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} + 144x^{2}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} - 288axe^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} + 144a^{2}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}}\right)}{dx}\\=&36e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} + 36xe^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}}(6*3x^{2} - 12a*2x - 6*2x + 12a + 0) + 324*4x^{3}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} + 324x^{4}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}}(6*3x^{2} - 12a*2x - 6*2x + 12a + 0) - 864a*3x^{2}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} - 864ax^{3}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}}(6*3x^{2} - 12a*2x - 6*2x + 12a + 0) - 432*3x^{2}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} - 432x^{3}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}}(6*3x^{2} - 12a*2x - 6*2x + 12a + 0) + 1008a*2xe^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} + 1008ax^{2}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}}(6*3x^{2} - 12a*2x - 6*2x + 12a + 0) - 24ae^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}}(6*3x^{2} - 12a*2x - 6*2x + 12a + 0) + 576a^{2}*2xe^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} + 576a^{2}x^{2}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}}(6*3x^{2} - 12a*2x - 6*2x + 12a + 0) - 576a^{2}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} - 576a^{2}xe^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}}(6*3x^{2} - 12a*2x - 6*2x + 12a + 0) - 12e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}}(6*3x^{2} - 12a*2x - 6*2x + 12a + 0) + 144*2xe^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} + 144x^{2}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}}(6*3x^{2} - 12a*2x - 6*2x + 12a + 0) - 288ae^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} - 288axe^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}}(6*3x^{2} - 12a*2x - 6*2x + 12a + 0) + 144a^{2}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}}(6*3x^{2} - 12a*2x - 6*2x + 12a + 0)\\=&36e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} + 216x^{3}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} + 1296ax^{2}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} - 1944x^{2}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} + 3024axe^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} + 5832x^{6}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} - 23328ax^{5}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} - 11664x^{5}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} + 42768ax^{4}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} + 31104a^{2}x^{4}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} - 51840a^{2}x^{3}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} + 7776x^{4}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} - 25920ax^{3}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} + 28512a^{2}x^{2}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} - 3456a^{2}xe^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} - 864a^{2}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} - 13824a^{3}x^{3}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} + 20736a^{3}x^{2}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} - 10368a^{3}xe^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} + 432xe^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} - 432ae^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} + 1728a^{3}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}}\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( 36e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} + 216x^{3}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} + 1296ax^{2}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} - 1944x^{2}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} + 3024axe^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} + 5832x^{6}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} - 23328ax^{5}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} - 11664x^{5}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} + 42768ax^{4}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} + 31104a^{2}x^{4}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} - 51840a^{2}x^{3}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} + 7776x^{4}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} - 25920ax^{3}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} + 28512a^{2}x^{2}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} - 3456a^{2}xe^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} - 864a^{2}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} - 13824a^{3}x^{3}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} + 20736a^{3}x^{2}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} - 10368a^{3}xe^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} + 432xe^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} - 432ae^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} + 1728a^{3}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}}\right)}{dx}\\=&36e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}}(6*3x^{2} - 12a*2x - 6*2x + 12a + 0) + 216*3x^{2}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} + 216x^{3}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}}(6*3x^{2} - 12a*2x - 6*2x + 12a + 0) + 1296a*2xe^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} + 1296ax^{2}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}}(6*3x^{2} - 12a*2x - 6*2x + 12a + 0) - 1944*2xe^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} - 1944x^{2}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}}(6*3x^{2} - 12a*2x - 6*2x + 12a + 0) + 3024ae^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} + 3024axe^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}}(6*3x^{2} - 12a*2x - 6*2x + 12a + 0) + 5832*6x^{5}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} + 5832x^{6}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}}(6*3x^{2} - 12a*2x - 6*2x + 12a + 0) - 23328a*5x^{4}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} - 23328ax^{5}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}}(6*3x^{2} - 12a*2x - 6*2x + 12a + 0) - 11664*5x^{4}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} - 11664x^{5}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}}(6*3x^{2} - 12a*2x - 6*2x + 12a + 0) + 42768a*4x^{3}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} + 42768ax^{4}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}}(6*3x^{2} - 12a*2x - 6*2x + 12a + 0) + 31104a^{2}*4x^{3}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} + 31104a^{2}x^{4}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}}(6*3x^{2} - 12a*2x - 6*2x + 12a + 0) - 51840a^{2}*3x^{2}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} - 51840a^{2}x^{3}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}}(6*3x^{2} - 12a*2x - 6*2x + 12a + 0) + 7776*4x^{3}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} + 7776x^{4}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}}(6*3x^{2} - 12a*2x - 6*2x + 12a + 0) - 25920a*3x^{2}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} - 25920ax^{3}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}}(6*3x^{2} - 12a*2x - 6*2x + 12a + 0) + 28512a^{2}*2xe^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} + 28512a^{2}x^{2}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}}(6*3x^{2} - 12a*2x - 6*2x + 12a + 0) - 3456a^{2}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} - 3456a^{2}xe^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}}(6*3x^{2} - 12a*2x - 6*2x + 12a + 0) - 864a^{2}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}}(6*3x^{2} - 12a*2x - 6*2x + 12a + 0) - 13824a^{3}*3x^{2}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} - 13824a^{3}x^{3}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}}(6*3x^{2} - 12a*2x - 6*2x + 12a + 0) + 20736a^{3}*2xe^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} + 20736a^{3}x^{2}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}}(6*3x^{2} - 12a*2x - 6*2x + 12a + 0) - 10368a^{3}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} - 10368a^{3}xe^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}}(6*3x^{2} - 12a*2x - 6*2x + 12a + 0) + 432e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} + 432xe^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}}(6*3x^{2} - 12a*2x - 6*2x + 12a + 0) - 432ae^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}}(6*3x^{2} - 12a*2x - 6*2x + 12a + 0) + 1728a^{3}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}}(6*3x^{2} - 12a*2x - 6*2x + 12a + 0)\\=&-3888x^{2}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} + 12096axe^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} - 4320xe^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} + 3456ae^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} - 54432x^{5}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} + 305856ax^{4}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} - 95904x^{4}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} + 259200ax^{3}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} - 622080a^{2}x^{3}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} - 186624a^{2}x^{2}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} + 62208x^{3}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} - 155520ax^{2}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} + 114048a^{2}xe^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} + 104976x^{8}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} - 559872ax^{7}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} - 279936x^{7}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} + 1399680ax^{6}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} + 1119744a^{2}x^{6}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} - 2612736a^{2}x^{5}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} + 279936x^{6}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} - 1306368ax^{5}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} + 2270592a^{2}x^{4}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} - 995328a^{3}x^{5}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} + 2156544a^{3}x^{4}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} - 1741824a^{3}x^{3}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} + 539136a^{3}x^{2}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} - 8640a^{2}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} - 20736a^{3}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} + 331776a^{4}x^{4}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} - 663552a^{4}x^{3}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} + 497664a^{4}x^{2}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} - 165888a^{4}xe^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} + 432e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}} + 20736a^{4}e^{6x^{3} - 12ax^{2} - 6x^{2} + 12ax + 16a^{2}}\\ \end{split}\end{equation} \]
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