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 b 求 4 阶导数。
注意，变量是区分大小写的。
\[ \begin{equation}\begin{split}【1/1】求函数({b}^{4} - 6{b}^{3} + 11{b}^{2} - 6b){a}^{b}{\frac{1}{a}}^{4} + sin(a)(cos(b)) 关于 b 的 4 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = \frac{b^{4}{a}^{b}}{a^{4}} - \frac{6b^{3}{a}^{b}}{a^{4}} + \frac{11b^{2}{a}^{b}}{a^{4}} - \frac{6b{a}^{b}}{a^{4}} + sin(a)cos(b)\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( \frac{b^{4}{a}^{b}}{a^{4}} - \frac{6b^{3}{a}^{b}}{a^{4}} + \frac{11b^{2}{a}^{b}}{a^{4}} - \frac{6b{a}^{b}}{a^{4}} + sin(a)cos(b)\right)}{db}\\=&\frac{4b^{3}{a}^{b}}{a^{4}} + \frac{b^{4}({a}^{b}((1)ln(a) + \frac{(b)(0)}{(a)}))}{a^{4}} - \frac{6*3b^{2}{a}^{b}}{a^{4}} - \frac{6b^{3}({a}^{b}((1)ln(a) + \frac{(b)(0)}{(a)}))}{a^{4}} + \frac{11*2b{a}^{b}}{a^{4}} + \frac{11b^{2}({a}^{b}((1)ln(a) + \frac{(b)(0)}{(a)}))}{a^{4}} - \frac{6{a}^{b}}{a^{4}} - \frac{6b({a}^{b}((1)ln(a) + \frac{(b)(0)}{(a)}))}{a^{4}} + cos(a)*0cos(b) + sin(a)*-sin(b)\\=&\frac{b^{4}{a}^{b}ln(a)}{a^{4}} - \frac{6b^{3}{a}^{b}ln(a)}{a^{4}} + \frac{11b^{2}{a}^{b}ln(a)}{a^{4}} - \frac{6b{a}^{b}ln(a)}{a^{4}} + \frac{22b{a}^{b}}{a^{4}} - \frac{18b^{2}{a}^{b}}{a^{4}} - \frac{6{a}^{b}}{a^{4}} + \frac{4b^{3}{a}^{b}}{a^{4}} - sin(b)sin(a)\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( \frac{b^{4}{a}^{b}ln(a)}{a^{4}} - \frac{6b^{3}{a}^{b}ln(a)}{a^{4}} + \frac{11b^{2}{a}^{b}ln(a)}{a^{4}} - \frac{6b{a}^{b}ln(a)}{a^{4}} + \frac{22b{a}^{b}}{a^{4}} - \frac{18b^{2}{a}^{b}}{a^{4}} - \frac{6{a}^{b}}{a^{4}} + \frac{4b^{3}{a}^{b}}{a^{4}} - sin(b)sin(a)\right)}{db}\\=&\frac{4b^{3}{a}^{b}ln(a)}{a^{4}} + \frac{b^{4}({a}^{b}((1)ln(a) + \frac{(b)(0)}{(a)}))ln(a)}{a^{4}} + \frac{b^{4}{a}^{b}*0}{a^{4}(a)} - \frac{6*3b^{2}{a}^{b}ln(a)}{a^{4}} - \frac{6b^{3}({a}^{b}((1)ln(a) + \frac{(b)(0)}{(a)}))ln(a)}{a^{4}} - \frac{6b^{3}{a}^{b}*0}{a^{4}(a)} + \frac{11*2b{a}^{b}ln(a)}{a^{4}} + \frac{11b^{2}({a}^{b}((1)ln(a) + \frac{(b)(0)}{(a)}))ln(a)}{a^{4}} + \frac{11b^{2}{a}^{b}*0}{a^{4}(a)} - \frac{6{a}^{b}ln(a)}{a^{4}} - \frac{6b({a}^{b}((1)ln(a) + \frac{(b)(0)}{(a)}))ln(a)}{a^{4}} - \frac{6b{a}^{b}*0}{a^{4}(a)} + \frac{22{a}^{b}}{a^{4}} + \frac{22b({a}^{b}((1)ln(a) + \frac{(b)(0)}{(a)}))}{a^{4}} - \frac{18*2b{a}^{b}}{a^{4}} - \frac{18b^{2}({a}^{b}((1)ln(a) + \frac{(b)(0)}{(a)}))}{a^{4}} - \frac{6({a}^{b}((1)ln(a) + \frac{(b)(0)}{(a)}))}{a^{4}} + \frac{4*3b^{2}{a}^{b}}{a^{4}} + \frac{4b^{3}({a}^{b}((1)ln(a) + \frac{(b)(0)}{(a)}))}{a^{4}} - cos(b)sin(a) - sin(b)cos(a)*0\\=&\frac{8b^{3}{a}^{b}ln(a)}{a^{4}} + \frac{b^{4}{a}^{b}ln^{2}(a)}{a^{4}} - \frac{36b^{2}{a}^{b}ln(a)}{a^{4}} - \frac{6b^{3}{a}^{b}ln^{2}(a)}{a^{4}} + \frac{44b{a}^{b}ln(a)}{a^{4}} + \frac{11b^{2}{a}^{b}ln^{2}(a)}{a^{4}} - \frac{12{a}^{b}ln(a)}{a^{4}} - \frac{6b{a}^{b}ln^{2}(a)}{a^{4}} + \frac{22{a}^{b}}{a^{4}} - \frac{36b{a}^{b}}{a^{4}} + \frac{12b^{2}{a}^{b}}{a^{4}} - sin(a)cos(b)\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( \frac{8b^{3}{a}^{b}ln(a)}{a^{4}} + \frac{b^{4}{a}^{b}ln^{2}(a)}{a^{4}} - \frac{36b^{2}{a}^{b}ln(a)}{a^{4}} - \frac{6b^{3}{a}^{b}ln^{2}(a)}{a^{4}} + \frac{44b{a}^{b}ln(a)}{a^{4}} + \frac{11b^{2}{a}^{b}ln^{2}(a)}{a^{4}} - \frac{12{a}^{b}ln(a)}{a^{4}} - \frac{6b{a}^{b}ln^{2}(a)}{a^{4}} + \frac{22{a}^{b}}{a^{4}} - \frac{36b{a}^{b}}{a^{4}} + \frac{12b^{2}{a}^{b}}{a^{4}} - sin(a)cos(b)\right)}{db}\\=&\frac{8*3b^{2}{a}^{b}ln(a)}{a^{4}} + \frac{8b^{3}({a}^{b}((1)ln(a) + \frac{(b)(0)}{(a)}))ln(a)}{a^{4}} + \frac{8b^{3}{a}^{b}*0}{a^{4}(a)} + \frac{4b^{3}{a}^{b}ln^{2}(a)}{a^{4}} + \frac{b^{4}({a}^{b}((1)ln(a) + \frac{(b)(0)}{(a)}))ln^{2}(a)}{a^{4}} + \frac{b^{4}{a}^{b}*2ln(a)*0}{a^{4}(a)} - \frac{36*2b{a}^{b}ln(a)}{a^{4}} - \frac{36b^{2}({a}^{b}((1)ln(a) + \frac{(b)(0)}{(a)}))ln(a)}{a^{4}} - \frac{36b^{2}{a}^{b}*0}{a^{4}(a)} - \frac{6*3b^{2}{a}^{b}ln^{2}(a)}{a^{4}} - \frac{6b^{3}({a}^{b}((1)ln(a) + \frac{(b)(0)}{(a)}))ln^{2}(a)}{a^{4}} - \frac{6b^{3}{a}^{b}*2ln(a)*0}{a^{4}(a)} + \frac{44{a}^{b}ln(a)}{a^{4}} + \frac{44b({a}^{b}((1)ln(a) + \frac{(b)(0)}{(a)}))ln(a)}{a^{4}} + \frac{44b{a}^{b}*0}{a^{4}(a)} + \frac{11*2b{a}^{b}ln^{2}(a)}{a^{4}} + \frac{11b^{2}({a}^{b}((1)ln(a) + \frac{(b)(0)}{(a)}))ln^{2}(a)}{a^{4}} + \frac{11b^{2}{a}^{b}*2ln(a)*0}{a^{4}(a)} - \frac{12({a}^{b}((1)ln(a) + \frac{(b)(0)}{(a)}))ln(a)}{a^{4}} - \frac{12{a}^{b}*0}{a^{4}(a)} - \frac{6{a}^{b}ln^{2}(a)}{a^{4}} - \frac{6b({a}^{b}((1)ln(a) + \frac{(b)(0)}{(a)}))ln^{2}(a)}{a^{4}} - \frac{6b{a}^{b}*2ln(a)*0}{a^{4}(a)} + \frac{22({a}^{b}((1)ln(a) + \frac{(b)(0)}{(a)}))}{a^{4}} - \frac{36{a}^{b}}{a^{4}} - \frac{36b({a}^{b}((1)ln(a) + \frac{(b)(0)}{(a)}))}{a^{4}} + \frac{12*2b{a}^{b}}{a^{4}} + \frac{12b^{2}({a}^{b}((1)ln(a) + \frac{(b)(0)}{(a)}))}{a^{4}} - cos(a)*0cos(b) - sin(a)*-sin(b)\\=&\frac{36b^{2}{a}^{b}ln(a)}{a^{4}} + \frac{12b^{3}{a}^{b}ln^{2}(a)}{a^{4}} + \frac{b^{4}{a}^{b}ln^{3}(a)}{a^{4}} - \frac{108b{a}^{b}ln(a)}{a^{4}} - \frac{54b^{2}{a}^{b}ln^{2}(a)}{a^{4}} - \frac{6b^{3}{a}^{b}ln^{3}(a)}{a^{4}} + \frac{66{a}^{b}ln(a)}{a^{4}} + \frac{66b{a}^{b}ln^{2}(a)}{a^{4}} + \frac{11b^{2}{a}^{b}ln^{3}(a)}{a^{4}} - \frac{18{a}^{b}ln^{2}(a)}{a^{4}} - \frac{6b{a}^{b}ln^{3}(a)}{a^{4}} - \frac{36{a}^{b}}{a^{4}} + \frac{24b{a}^{b}}{a^{4}} + sin(b)sin(a)\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( \frac{36b^{2}{a}^{b}ln(a)}{a^{4}} + \frac{12b^{3}{a}^{b}ln^{2}(a)}{a^{4}} + \frac{b^{4}{a}^{b}ln^{3}(a)}{a^{4}} - \frac{108b{a}^{b}ln(a)}{a^{4}} - \frac{54b^{2}{a}^{b}ln^{2}(a)}{a^{4}} - \frac{6b^{3}{a}^{b}ln^{3}(a)}{a^{4}} + \frac{66{a}^{b}ln(a)}{a^{4}} + \frac{66b{a}^{b}ln^{2}(a)}{a^{4}} + \frac{11b^{2}{a}^{b}ln^{3}(a)}{a^{4}} - \frac{18{a}^{b}ln^{2}(a)}{a^{4}} - \frac{6b{a}^{b}ln^{3}(a)}{a^{4}} - \frac{36{a}^{b}}{a^{4}} + \frac{24b{a}^{b}}{a^{4}} + sin(b)sin(a)\right)}{db}\\=&\frac{36*2b{a}^{b}ln(a)}{a^{4}} + \frac{36b^{2}({a}^{b}((1)ln(a) + \frac{(b)(0)}{(a)}))ln(a)}{a^{4}} + \frac{36b^{2}{a}^{b}*0}{a^{4}(a)} + \frac{12*3b^{2}{a}^{b}ln^{2}(a)}{a^{4}} + \frac{12b^{3}({a}^{b}((1)ln(a) + \frac{(b)(0)}{(a)}))ln^{2}(a)}{a^{4}} + \frac{12b^{3}{a}^{b}*2ln(a)*0}{a^{4}(a)} + \frac{4b^{3}{a}^{b}ln^{3}(a)}{a^{4}} + \frac{b^{4}({a}^{b}((1)ln(a) + \frac{(b)(0)}{(a)}))ln^{3}(a)}{a^{4}} + \frac{b^{4}{a}^{b}*3ln^{2}(a)*0}{a^{4}(a)} - \frac{108{a}^{b}ln(a)}{a^{4}} - \frac{108b({a}^{b}((1)ln(a) + \frac{(b)(0)}{(a)}))ln(a)}{a^{4}} - \frac{108b{a}^{b}*0}{a^{4}(a)} - \frac{54*2b{a}^{b}ln^{2}(a)}{a^{4}} - \frac{54b^{2}({a}^{b}((1)ln(a) + \frac{(b)(0)}{(a)}))ln^{2}(a)}{a^{4}} - \frac{54b^{2}{a}^{b}*2ln(a)*0}{a^{4}(a)} - \frac{6*3b^{2}{a}^{b}ln^{3}(a)}{a^{4}} - \frac{6b^{3}({a}^{b}((1)ln(a) + \frac{(b)(0)}{(a)}))ln^{3}(a)}{a^{4}} - \frac{6b^{3}{a}^{b}*3ln^{2}(a)*0}{a^{4}(a)} + \frac{66({a}^{b}((1)ln(a) + \frac{(b)(0)}{(a)}))ln(a)}{a^{4}} + \frac{66{a}^{b}*0}{a^{4}(a)} + \frac{66{a}^{b}ln^{2}(a)}{a^{4}} + \frac{66b({a}^{b}((1)ln(a) + \frac{(b)(0)}{(a)}))ln^{2}(a)}{a^{4}} + \frac{66b{a}^{b}*2ln(a)*0}{a^{4}(a)} + \frac{11*2b{a}^{b}ln^{3}(a)}{a^{4}} + \frac{11b^{2}({a}^{b}((1)ln(a) + \frac{(b)(0)}{(a)}))ln^{3}(a)}{a^{4}} + \frac{11b^{2}{a}^{b}*3ln^{2}(a)*0}{a^{4}(a)} - \frac{18({a}^{b}((1)ln(a) + \frac{(b)(0)}{(a)}))ln^{2}(a)}{a^{4}} - \frac{18{a}^{b}*2ln(a)*0}{a^{4}(a)} - \frac{6{a}^{b}ln^{3}(a)}{a^{4}} - \frac{6b({a}^{b}((1)ln(a) + \frac{(b)(0)}{(a)}))ln^{3}(a)}{a^{4}} - \frac{6b{a}^{b}*3ln^{2}(a)*0}{a^{4}(a)} - \frac{36({a}^{b}((1)ln(a) + \frac{(b)(0)}{(a)}))}{a^{4}} + \frac{24{a}^{b}}{a^{4}} + \frac{24b({a}^{b}((1)ln(a) + \frac{(b)(0)}{(a)}))}{a^{4}} + cos(b)sin(a) + sin(b)cos(a)*0\\=&\frac{96b{a}^{b}ln(a)}{a^{4}} + \frac{72b^{2}{a}^{b}ln^{2}(a)}{a^{4}} + \frac{16b^{3}{a}^{b}ln^{3}(a)}{a^{4}} + \frac{b^{4}{a}^{b}ln^{4}(a)}{a^{4}} - \frac{144{a}^{b}ln(a)}{a^{4}} - \frac{216b{a}^{b}ln^{2}(a)}{a^{4}} - \frac{72b^{2}{a}^{b}ln^{3}(a)}{a^{4}} - \frac{6b^{3}{a}^{b}ln^{4}(a)}{a^{4}} + \frac{132{a}^{b}ln^{2}(a)}{a^{4}} + \frac{88b{a}^{b}ln^{3}(a)}{a^{4}} + \frac{11b^{2}{a}^{b}ln^{4}(a)}{a^{4}} - \frac{24{a}^{b}ln^{3}(a)}{a^{4}} - \frac{6b{a}^{b}ln^{4}(a)}{a^{4}} + \frac{24{a}^{b}}{a^{4}} + sin(a)cos(b)\\ \end{split}\end{equation} \]
注意，变量是区分大小写的。
\[ \begin{equation}\begin{split}【1/1】求函数({b}^{4} - 6{b}^{3} + 11{b}^{2} - 6b){a}^{b}{\frac{1}{a}}^{4} + sin(a)(cos(b)) 关于 b 的 4 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = \frac{b^{4}{a}^{b}}{a^{4}} - \frac{6b^{3}{a}^{b}}{a^{4}} + \frac{11b^{2}{a}^{b}}{a^{4}} - \frac{6b{a}^{b}}{a^{4}} + sin(a)cos(b)\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( \frac{b^{4}{a}^{b}}{a^{4}} - \frac{6b^{3}{a}^{b}}{a^{4}} + \frac{11b^{2}{a}^{b}}{a^{4}} - \frac{6b{a}^{b}}{a^{4}} + sin(a)cos(b)\right)}{db}\\=&\frac{4b^{3}{a}^{b}}{a^{4}} + \frac{b^{4}({a}^{b}((1)ln(a) + \frac{(b)(0)}{(a)}))}{a^{4}} - \frac{6*3b^{2}{a}^{b}}{a^{4}} - \frac{6b^{3}({a}^{b}((1)ln(a) + \frac{(b)(0)}{(a)}))}{a^{4}} + \frac{11*2b{a}^{b}}{a^{4}} + \frac{11b^{2}({a}^{b}((1)ln(a) + \frac{(b)(0)}{(a)}))}{a^{4}} - \frac{6{a}^{b}}{a^{4}} - \frac{6b({a}^{b}((1)ln(a) + \frac{(b)(0)}{(a)}))}{a^{4}} + cos(a)*0cos(b) + sin(a)*-sin(b)\\=&\frac{b^{4}{a}^{b}ln(a)}{a^{4}} - \frac{6b^{3}{a}^{b}ln(a)}{a^{4}} + \frac{11b^{2}{a}^{b}ln(a)}{a^{4}} - \frac{6b{a}^{b}ln(a)}{a^{4}} + \frac{22b{a}^{b}}{a^{4}} - \frac{18b^{2}{a}^{b}}{a^{4}} - \frac{6{a}^{b}}{a^{4}} + \frac{4b^{3}{a}^{b}}{a^{4}} - sin(b)sin(a)\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( \frac{b^{4}{a}^{b}ln(a)}{a^{4}} - \frac{6b^{3}{a}^{b}ln(a)}{a^{4}} + \frac{11b^{2}{a}^{b}ln(a)}{a^{4}} - \frac{6b{a}^{b}ln(a)}{a^{4}} + \frac{22b{a}^{b}}{a^{4}} - \frac{18b^{2}{a}^{b}}{a^{4}} - \frac{6{a}^{b}}{a^{4}} + \frac{4b^{3}{a}^{b}}{a^{4}} - sin(b)sin(a)\right)}{db}\\=&\frac{4b^{3}{a}^{b}ln(a)}{a^{4}} + \frac{b^{4}({a}^{b}((1)ln(a) + \frac{(b)(0)}{(a)}))ln(a)}{a^{4}} + \frac{b^{4}{a}^{b}*0}{a^{4}(a)} - \frac{6*3b^{2}{a}^{b}ln(a)}{a^{4}} - \frac{6b^{3}({a}^{b}((1)ln(a) + \frac{(b)(0)}{(a)}))ln(a)}{a^{4}} - \frac{6b^{3}{a}^{b}*0}{a^{4}(a)} + \frac{11*2b{a}^{b}ln(a)}{a^{4}} + \frac{11b^{2}({a}^{b}((1)ln(a) + \frac{(b)(0)}{(a)}))ln(a)}{a^{4}} + \frac{11b^{2}{a}^{b}*0}{a^{4}(a)} - \frac{6{a}^{b}ln(a)}{a^{4}} - \frac{6b({a}^{b}((1)ln(a) + \frac{(b)(0)}{(a)}))ln(a)}{a^{4}} - \frac{6b{a}^{b}*0}{a^{4}(a)} + \frac{22{a}^{b}}{a^{4}} + \frac{22b({a}^{b}((1)ln(a) + \frac{(b)(0)}{(a)}))}{a^{4}} - \frac{18*2b{a}^{b}}{a^{4}} - \frac{18b^{2}({a}^{b}((1)ln(a) + \frac{(b)(0)}{(a)}))}{a^{4}} - \frac{6({a}^{b}((1)ln(a) + \frac{(b)(0)}{(a)}))}{a^{4}} + \frac{4*3b^{2}{a}^{b}}{a^{4}} + \frac{4b^{3}({a}^{b}((1)ln(a) + \frac{(b)(0)}{(a)}))}{a^{4}} - cos(b)sin(a) - sin(b)cos(a)*0\\=&\frac{8b^{3}{a}^{b}ln(a)}{a^{4}} + \frac{b^{4}{a}^{b}ln^{2}(a)}{a^{4}} - \frac{36b^{2}{a}^{b}ln(a)}{a^{4}} - \frac{6b^{3}{a}^{b}ln^{2}(a)}{a^{4}} + \frac{44b{a}^{b}ln(a)}{a^{4}} + \frac{11b^{2}{a}^{b}ln^{2}(a)}{a^{4}} - \frac{12{a}^{b}ln(a)}{a^{4}} - \frac{6b{a}^{b}ln^{2}(a)}{a^{4}} + \frac{22{a}^{b}}{a^{4}} - \frac{36b{a}^{b}}{a^{4}} + \frac{12b^{2}{a}^{b}}{a^{4}} - sin(a)cos(b)\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( \frac{8b^{3}{a}^{b}ln(a)}{a^{4}} + \frac{b^{4}{a}^{b}ln^{2}(a)}{a^{4}} - \frac{36b^{2}{a}^{b}ln(a)}{a^{4}} - \frac{6b^{3}{a}^{b}ln^{2}(a)}{a^{4}} + \frac{44b{a}^{b}ln(a)}{a^{4}} + \frac{11b^{2}{a}^{b}ln^{2}(a)}{a^{4}} - \frac{12{a}^{b}ln(a)}{a^{4}} - \frac{6b{a}^{b}ln^{2}(a)}{a^{4}} + \frac{22{a}^{b}}{a^{4}} - \frac{36b{a}^{b}}{a^{4}} + \frac{12b^{2}{a}^{b}}{a^{4}} - sin(a)cos(b)\right)}{db}\\=&\frac{8*3b^{2}{a}^{b}ln(a)}{a^{4}} + \frac{8b^{3}({a}^{b}((1)ln(a) + \frac{(b)(0)}{(a)}))ln(a)}{a^{4}} + \frac{8b^{3}{a}^{b}*0}{a^{4}(a)} + \frac{4b^{3}{a}^{b}ln^{2}(a)}{a^{4}} + \frac{b^{4}({a}^{b}((1)ln(a) + \frac{(b)(0)}{(a)}))ln^{2}(a)}{a^{4}} + \frac{b^{4}{a}^{b}*2ln(a)*0}{a^{4}(a)} - \frac{36*2b{a}^{b}ln(a)}{a^{4}} - \frac{36b^{2}({a}^{b}((1)ln(a) + \frac{(b)(0)}{(a)}))ln(a)}{a^{4}} - \frac{36b^{2}{a}^{b}*0}{a^{4}(a)} - \frac{6*3b^{2}{a}^{b}ln^{2}(a)}{a^{4}} - \frac{6b^{3}({a}^{b}((1)ln(a) + \frac{(b)(0)}{(a)}))ln^{2}(a)}{a^{4}} - \frac{6b^{3}{a}^{b}*2ln(a)*0}{a^{4}(a)} + \frac{44{a}^{b}ln(a)}{a^{4}} + \frac{44b({a}^{b}((1)ln(a) + \frac{(b)(0)}{(a)}))ln(a)}{a^{4}} + \frac{44b{a}^{b}*0}{a^{4}(a)} + \frac{11*2b{a}^{b}ln^{2}(a)}{a^{4}} + \frac{11b^{2}({a}^{b}((1)ln(a) + \frac{(b)(0)}{(a)}))ln^{2}(a)}{a^{4}} + \frac{11b^{2}{a}^{b}*2ln(a)*0}{a^{4}(a)} - \frac{12({a}^{b}((1)ln(a) + \frac{(b)(0)}{(a)}))ln(a)}{a^{4}} - \frac{12{a}^{b}*0}{a^{4}(a)} - \frac{6{a}^{b}ln^{2}(a)}{a^{4}} - \frac{6b({a}^{b}((1)ln(a) + \frac{(b)(0)}{(a)}))ln^{2}(a)}{a^{4}} - \frac{6b{a}^{b}*2ln(a)*0}{a^{4}(a)} + \frac{22({a}^{b}((1)ln(a) + \frac{(b)(0)}{(a)}))}{a^{4}} - \frac{36{a}^{b}}{a^{4}} - \frac{36b({a}^{b}((1)ln(a) + \frac{(b)(0)}{(a)}))}{a^{4}} + \frac{12*2b{a}^{b}}{a^{4}} + \frac{12b^{2}({a}^{b}((1)ln(a) + \frac{(b)(0)}{(a)}))}{a^{4}} - cos(a)*0cos(b) - sin(a)*-sin(b)\\=&\frac{36b^{2}{a}^{b}ln(a)}{a^{4}} + \frac{12b^{3}{a}^{b}ln^{2}(a)}{a^{4}} + \frac{b^{4}{a}^{b}ln^{3}(a)}{a^{4}} - \frac{108b{a}^{b}ln(a)}{a^{4}} - \frac{54b^{2}{a}^{b}ln^{2}(a)}{a^{4}} - \frac{6b^{3}{a}^{b}ln^{3}(a)}{a^{4}} + \frac{66{a}^{b}ln(a)}{a^{4}} + \frac{66b{a}^{b}ln^{2}(a)}{a^{4}} + \frac{11b^{2}{a}^{b}ln^{3}(a)}{a^{4}} - \frac{18{a}^{b}ln^{2}(a)}{a^{4}} - \frac{6b{a}^{b}ln^{3}(a)}{a^{4}} - \frac{36{a}^{b}}{a^{4}} + \frac{24b{a}^{b}}{a^{4}} + sin(b)sin(a)\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( \frac{36b^{2}{a}^{b}ln(a)}{a^{4}} + \frac{12b^{3}{a}^{b}ln^{2}(a)}{a^{4}} + \frac{b^{4}{a}^{b}ln^{3}(a)}{a^{4}} - \frac{108b{a}^{b}ln(a)}{a^{4}} - \frac{54b^{2}{a}^{b}ln^{2}(a)}{a^{4}} - \frac{6b^{3}{a}^{b}ln^{3}(a)}{a^{4}} + \frac{66{a}^{b}ln(a)}{a^{4}} + \frac{66b{a}^{b}ln^{2}(a)}{a^{4}} + \frac{11b^{2}{a}^{b}ln^{3}(a)}{a^{4}} - \frac{18{a}^{b}ln^{2}(a)}{a^{4}} - \frac{6b{a}^{b}ln^{3}(a)}{a^{4}} - \frac{36{a}^{b}}{a^{4}} + \frac{24b{a}^{b}}{a^{4}} + sin(b)sin(a)\right)}{db}\\=&\frac{36*2b{a}^{b}ln(a)}{a^{4}} + \frac{36b^{2}({a}^{b}((1)ln(a) + \frac{(b)(0)}{(a)}))ln(a)}{a^{4}} + \frac{36b^{2}{a}^{b}*0}{a^{4}(a)} + \frac{12*3b^{2}{a}^{b}ln^{2}(a)}{a^{4}} + \frac{12b^{3}({a}^{b}((1)ln(a) + \frac{(b)(0)}{(a)}))ln^{2}(a)}{a^{4}} + \frac{12b^{3}{a}^{b}*2ln(a)*0}{a^{4}(a)} + \frac{4b^{3}{a}^{b}ln^{3}(a)}{a^{4}} + \frac{b^{4}({a}^{b}((1)ln(a) + \frac{(b)(0)}{(a)}))ln^{3}(a)}{a^{4}} + \frac{b^{4}{a}^{b}*3ln^{2}(a)*0}{a^{4}(a)} - \frac{108{a}^{b}ln(a)}{a^{4}} - \frac{108b({a}^{b}((1)ln(a) + \frac{(b)(0)}{(a)}))ln(a)}{a^{4}} - \frac{108b{a}^{b}*0}{a^{4}(a)} - \frac{54*2b{a}^{b}ln^{2}(a)}{a^{4}} - \frac{54b^{2}({a}^{b}((1)ln(a) + \frac{(b)(0)}{(a)}))ln^{2}(a)}{a^{4}} - \frac{54b^{2}{a}^{b}*2ln(a)*0}{a^{4}(a)} - \frac{6*3b^{2}{a}^{b}ln^{3}(a)}{a^{4}} - \frac{6b^{3}({a}^{b}((1)ln(a) + \frac{(b)(0)}{(a)}))ln^{3}(a)}{a^{4}} - \frac{6b^{3}{a}^{b}*3ln^{2}(a)*0}{a^{4}(a)} + \frac{66({a}^{b}((1)ln(a) + \frac{(b)(0)}{(a)}))ln(a)}{a^{4}} + \frac{66{a}^{b}*0}{a^{4}(a)} + \frac{66{a}^{b}ln^{2}(a)}{a^{4}} + \frac{66b({a}^{b}((1)ln(a) + \frac{(b)(0)}{(a)}))ln^{2}(a)}{a^{4}} + \frac{66b{a}^{b}*2ln(a)*0}{a^{4}(a)} + \frac{11*2b{a}^{b}ln^{3}(a)}{a^{4}} + \frac{11b^{2}({a}^{b}((1)ln(a) + \frac{(b)(0)}{(a)}))ln^{3}(a)}{a^{4}} + \frac{11b^{2}{a}^{b}*3ln^{2}(a)*0}{a^{4}(a)} - \frac{18({a}^{b}((1)ln(a) + \frac{(b)(0)}{(a)}))ln^{2}(a)}{a^{4}} - \frac{18{a}^{b}*2ln(a)*0}{a^{4}(a)} - \frac{6{a}^{b}ln^{3}(a)}{a^{4}} - \frac{6b({a}^{b}((1)ln(a) + \frac{(b)(0)}{(a)}))ln^{3}(a)}{a^{4}} - \frac{6b{a}^{b}*3ln^{2}(a)*0}{a^{4}(a)} - \frac{36({a}^{b}((1)ln(a) + \frac{(b)(0)}{(a)}))}{a^{4}} + \frac{24{a}^{b}}{a^{4}} + \frac{24b({a}^{b}((1)ln(a) + \frac{(b)(0)}{(a)}))}{a^{4}} + cos(b)sin(a) + sin(b)cos(a)*0\\=&\frac{96b{a}^{b}ln(a)}{a^{4}} + \frac{72b^{2}{a}^{b}ln^{2}(a)}{a^{4}} + \frac{16b^{3}{a}^{b}ln^{3}(a)}{a^{4}} + \frac{b^{4}{a}^{b}ln^{4}(a)}{a^{4}} - \frac{144{a}^{b}ln(a)}{a^{4}} - \frac{216b{a}^{b}ln^{2}(a)}{a^{4}} - \frac{72b^{2}{a}^{b}ln^{3}(a)}{a^{4}} - \frac{6b^{3}{a}^{b}ln^{4}(a)}{a^{4}} + \frac{132{a}^{b}ln^{2}(a)}{a^{4}} + \frac{88b{a}^{b}ln^{3}(a)}{a^{4}} + \frac{11b^{2}{a}^{b}ln^{4}(a)}{a^{4}} - \frac{24{a}^{b}ln^{3}(a)}{a^{4}} - \frac{6b{a}^{b}ln^{4}(a)}{a^{4}} + \frac{24{a}^{b}}{a^{4}} + sin(a)cos(b)\\ \end{split}\end{equation} \]
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