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。
\[ \begin{equation}\begin{split}【1/1】求函数{4}^{(4 + {1}^{{(\frac{1}{(x - 1)})}^{2}})} 关于 x 的 4 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = {4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( {4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}\right)}{dx}\\=&({4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}((({1}^{\frac{1}{(x - 1)^{2}}}(((\frac{-2(1 + 0)}{(x - 1)^{3}}))ln(1) + \frac{(\frac{1}{(x - 1)^{2}})(0)}{(1)})) + 0)ln(4) + \frac{({1}^{\frac{1}{(x - 1)^{2}}} + 4)(0)}{(4)}))\\=&\frac{-2 * {1}^{\frac{1}{(x - 1)^{2}}}{4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}ln(4)ln(1)}{(x - 1)^{3}}\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( \frac{-2 * {1}^{\frac{1}{(x - 1)^{2}}}{4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}ln(4)ln(1)}{(x - 1)^{3}}\right)}{dx}\\=&-2(\frac{-3(1 + 0)}{(x - 1)^{4}}){1}^{\frac{1}{(x - 1)^{2}}}{4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}ln(4)ln(1) - \frac{2({1}^{\frac{1}{(x - 1)^{2}}}(((\frac{-2(1 + 0)}{(x - 1)^{3}}))ln(1) + \frac{(\frac{1}{(x - 1)^{2}})(0)}{(1)})){4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}ln(4)ln(1)}{(x - 1)^{3}} - \frac{2 * {1}^{\frac{1}{(x - 1)^{2}}}({4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}((({1}^{\frac{1}{(x - 1)^{2}}}(((\frac{-2(1 + 0)}{(x - 1)^{3}}))ln(1) + \frac{(\frac{1}{(x - 1)^{2}})(0)}{(1)})) + 0)ln(4) + \frac{({1}^{\frac{1}{(x - 1)^{2}}} + 4)(0)}{(4)}))ln(4)ln(1)}{(x - 1)^{3}} - \frac{2 * {1}^{\frac{1}{(x - 1)^{2}}}{4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}*0ln(1)}{(x - 1)^{3}(4)} - \frac{2 * {1}^{\frac{1}{(x - 1)^{2}}}{4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}ln(4)*0}{(x - 1)^{3}(1)}\\=&\frac{6 * {1}^{\frac{1}{(x - 1)^{2}}}{4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}ln(4)ln(1)}{(x - 1)^{4}} + \frac{4 * {1}^{\frac{1}{(x - 1)^{2}}}{4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}ln^{2}(1)ln(4)}{(x - 1)^{6}} + \frac{4 * {1}^{(2(\frac{1}{(x - 1)^{2}}))}{4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}ln^{2}(1)ln^{2}(4)}{(x - 1)^{6}}\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( \frac{6 * {1}^{\frac{1}{(x - 1)^{2}}}{4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}ln(4)ln(1)}{(x - 1)^{4}} + \frac{4 * {1}^{\frac{1}{(x - 1)^{2}}}{4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}ln^{2}(1)ln(4)}{(x - 1)^{6}} + \frac{4 * {1}^{(2(\frac{1}{(x - 1)^{2}}))}{4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}ln^{2}(1)ln^{2}(4)}{(x - 1)^{6}}\right)}{dx}\\=&6(\frac{-4(1 + 0)}{(x - 1)^{5}}){1}^{\frac{1}{(x - 1)^{2}}}{4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}ln(4)ln(1) + \frac{6({1}^{\frac{1}{(x - 1)^{2}}}(((\frac{-2(1 + 0)}{(x - 1)^{3}}))ln(1) + \frac{(\frac{1}{(x - 1)^{2}})(0)}{(1)})){4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}ln(4)ln(1)}{(x - 1)^{4}} + \frac{6 * {1}^{\frac{1}{(x - 1)^{2}}}({4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}((({1}^{\frac{1}{(x - 1)^{2}}}(((\frac{-2(1 + 0)}{(x - 1)^{3}}))ln(1) + \frac{(\frac{1}{(x - 1)^{2}})(0)}{(1)})) + 0)ln(4) + \frac{({1}^{\frac{1}{(x - 1)^{2}}} + 4)(0)}{(4)}))ln(4)ln(1)}{(x - 1)^{4}} + \frac{6 * {1}^{\frac{1}{(x - 1)^{2}}}{4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}*0ln(1)}{(x - 1)^{4}(4)} + \frac{6 * {1}^{\frac{1}{(x - 1)^{2}}}{4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}ln(4)*0}{(x - 1)^{4}(1)} + 4(\frac{-6(1 + 0)}{(x - 1)^{7}}){1}^{\frac{1}{(x - 1)^{2}}}{4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}ln^{2}(1)ln(4) + \frac{4({1}^{\frac{1}{(x - 1)^{2}}}(((\frac{-2(1 + 0)}{(x - 1)^{3}}))ln(1) + \frac{(\frac{1}{(x - 1)^{2}})(0)}{(1)})){4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}ln^{2}(1)ln(4)}{(x - 1)^{6}} + \frac{4 * {1}^{\frac{1}{(x - 1)^{2}}}({4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}((({1}^{\frac{1}{(x - 1)^{2}}}(((\frac{-2(1 + 0)}{(x - 1)^{3}}))ln(1) + \frac{(\frac{1}{(x - 1)^{2}})(0)}{(1)})) + 0)ln(4) + \frac{({1}^{\frac{1}{(x - 1)^{2}}} + 4)(0)}{(4)}))ln^{2}(1)ln(4)}{(x - 1)^{6}} + \frac{4 * {1}^{\frac{1}{(x - 1)^{2}}}{4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}*2ln(1)*0ln(4)}{(x - 1)^{6}(1)} + \frac{4 * {1}^{\frac{1}{(x - 1)^{2}}}{4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}ln^{2}(1)*0}{(x - 1)^{6}(4)} + 4(\frac{-6(1 + 0)}{(x - 1)^{7}}){1}^{(2(\frac{1}{(x - 1)^{2}}))}{4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}ln^{2}(1)ln^{2}(4) + \frac{4({1}^{(2(\frac{1}{(x - 1)^{2}}))}((2((\frac{-2(1 + 0)}{(x - 1)^{3}})))ln(1) + \frac{(2(\frac{1}{(x - 1)^{2}}))(0)}{(1)})){4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}ln^{2}(1)ln^{2}(4)}{(x - 1)^{6}} + \frac{4 * {1}^{(2(\frac{1}{(x - 1)^{2}}))}({4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}((({1}^{\frac{1}{(x - 1)^{2}}}(((\frac{-2(1 + 0)}{(x - 1)^{3}}))ln(1) + \frac{(\frac{1}{(x - 1)^{2}})(0)}{(1)})) + 0)ln(4) + \frac{({1}^{\frac{1}{(x - 1)^{2}}} + 4)(0)}{(4)}))ln^{2}(1)ln^{2}(4)}{(x - 1)^{6}} + \frac{4 * {1}^{(2(\frac{1}{(x - 1)^{2}}))}{4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}*2ln(1)*0ln^{2}(4)}{(x - 1)^{6}(1)} + \frac{4 * {1}^{(2(\frac{1}{(x - 1)^{2}}))}{4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}ln^{2}(1)*2ln(4)*0}{(x - 1)^{6}(4)}\\=&\frac{-24 * {1}^{\frac{1}{(x - 1)^{2}}}{4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}ln(4)ln(1)}{(x - 1)^{5}} - \frac{36 * {1}^{\frac{1}{(x - 1)^{2}}}{4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}ln^{2}(1)ln(4)}{(x - 1)^{7}} - \frac{12 * {1}^{(2(\frac{1}{(x - 1)^{2}}))}{4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}ln^{2}(1)ln^{2}(4)}{(x - 1)^{7}} - \frac{8 * {1}^{\frac{1}{(x - 1)^{2}}}{4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}ln^{3}(1)ln(4)}{(x - 1)^{9}} - \frac{8 * {1}^{(2(\frac{1}{(x - 1)^{2}}))}{4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}ln^{3}(1)ln^{2}(4)}{(x - 1)^{9}} - \frac{24 * {1}^{(\frac{2}{(x - 1)^{2}})}{4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}ln^{2}(1)ln^{2}(4)}{(x - 1)^{7}} - \frac{16 * {1}^{(\frac{2}{(x - 1)^{2}})}{4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}ln^{3}(1)ln^{2}(4)}{(x - 1)^{9}} - \frac{8 * {1}^{(\frac{3}{(x - 1)^{2}})}{4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}ln^{3}(1)ln^{3}(4)}{(x - 1)^{9}}\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( \frac{-24 * {1}^{\frac{1}{(x - 1)^{2}}}{4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}ln(4)ln(1)}{(x - 1)^{5}} - \frac{36 * {1}^{\frac{1}{(x - 1)^{2}}}{4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}ln^{2}(1)ln(4)}{(x - 1)^{7}} - \frac{12 * {1}^{(2(\frac{1}{(x - 1)^{2}}))}{4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}ln^{2}(1)ln^{2}(4)}{(x - 1)^{7}} - \frac{8 * {1}^{\frac{1}{(x - 1)^{2}}}{4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}ln^{3}(1)ln(4)}{(x - 1)^{9}} - \frac{8 * {1}^{(2(\frac{1}{(x - 1)^{2}}))}{4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}ln^{3}(1)ln^{2}(4)}{(x - 1)^{9}} - \frac{24 * {1}^{(\frac{2}{(x - 1)^{2}})}{4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}ln^{2}(1)ln^{2}(4)}{(x - 1)^{7}} - \frac{16 * {1}^{(\frac{2}{(x - 1)^{2}})}{4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}ln^{3}(1)ln^{2}(4)}{(x - 1)^{9}} - \frac{8 * {1}^{(\frac{3}{(x - 1)^{2}})}{4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}ln^{3}(1)ln^{3}(4)}{(x - 1)^{9}}\right)}{dx}\\=&-24(\frac{-5(1 + 0)}{(x - 1)^{6}}){1}^{\frac{1}{(x - 1)^{2}}}{4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}ln(4)ln(1) - \frac{24({1}^{\frac{1}{(x - 1)^{2}}}(((\frac{-2(1 + 0)}{(x - 1)^{3}}))ln(1) + \frac{(\frac{1}{(x - 1)^{2}})(0)}{(1)})){4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}ln(4)ln(1)}{(x - 1)^{5}} - \frac{24 * {1}^{\frac{1}{(x - 1)^{2}}}({4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}((({1}^{\frac{1}{(x - 1)^{2}}}(((\frac{-2(1 + 0)}{(x - 1)^{3}}))ln(1) + \frac{(\frac{1}{(x - 1)^{2}})(0)}{(1)})) + 0)ln(4) + \frac{({1}^{\frac{1}{(x - 1)^{2}}} + 4)(0)}{(4)}))ln(4)ln(1)}{(x - 1)^{5}} - \frac{24 * {1}^{\frac{1}{(x - 1)^{2}}}{4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}*0ln(1)}{(x - 1)^{5}(4)} - \frac{24 * {1}^{\frac{1}{(x - 1)^{2}}}{4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}ln(4)*0}{(x - 1)^{5}(1)} - 36(\frac{-7(1 + 0)}{(x - 1)^{8}}){1}^{\frac{1}{(x - 1)^{2}}}{4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}ln^{2}(1)ln(4) - \frac{36({1}^{\frac{1}{(x - 1)^{2}}}(((\frac{-2(1 + 0)}{(x - 1)^{3}}))ln(1) + \frac{(\frac{1}{(x - 1)^{2}})(0)}{(1)})){4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}ln^{2}(1)ln(4)}{(x - 1)^{7}} - \frac{36 * {1}^{\frac{1}{(x - 1)^{2}}}({4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}((({1}^{\frac{1}{(x - 1)^{2}}}(((\frac{-2(1 + 0)}{(x - 1)^{3}}))ln(1) + \frac{(\frac{1}{(x - 1)^{2}})(0)}{(1)})) + 0)ln(4) + \frac{({1}^{\frac{1}{(x - 1)^{2}}} + 4)(0)}{(4)}))ln^{2}(1)ln(4)}{(x - 1)^{7}} - \frac{36 * {1}^{\frac{1}{(x - 1)^{2}}}{4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}*2ln(1)*0ln(4)}{(x - 1)^{7}(1)} - \frac{36 * {1}^{\frac{1}{(x - 1)^{2}}}{4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}ln^{2}(1)*0}{(x - 1)^{7}(4)} - 12(\frac{-7(1 + 0)}{(x - 1)^{8}}){1}^{(2(\frac{1}{(x - 1)^{2}}))}{4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}ln^{2}(1)ln^{2}(4) - \frac{12({1}^{(2(\frac{1}{(x - 1)^{2}}))}((2((\frac{-2(1 + 0)}{(x - 1)^{3}})))ln(1) + \frac{(2(\frac{1}{(x - 1)^{2}}))(0)}{(1)})){4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}ln^{2}(1)ln^{2}(4)}{(x - 1)^{7}} - \frac{12 * {1}^{(2(\frac{1}{(x - 1)^{2}}))}({4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}((({1}^{\frac{1}{(x - 1)^{2}}}(((\frac{-2(1 + 0)}{(x - 1)^{3}}))ln(1) + \frac{(\frac{1}{(x - 1)^{2}})(0)}{(1)})) + 0)ln(4) + \frac{({1}^{\frac{1}{(x - 1)^{2}}} + 4)(0)}{(4)}))ln^{2}(1)ln^{2}(4)}{(x - 1)^{7}} - \frac{12 * {1}^{(2(\frac{1}{(x - 1)^{2}}))}{4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}*2ln(1)*0ln^{2}(4)}{(x - 1)^{7}(1)} - \frac{12 * {1}^{(2(\frac{1}{(x - 1)^{2}}))}{4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}ln^{2}(1)*2ln(4)*0}{(x - 1)^{7}(4)} - 8(\frac{-9(1 + 0)}{(x - 1)^{10}}){1}^{\frac{1}{(x - 1)^{2}}}{4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}ln^{3}(1)ln(4) - \frac{8({1}^{\frac{1}{(x - 1)^{2}}}(((\frac{-2(1 + 0)}{(x - 1)^{3}}))ln(1) + \frac{(\frac{1}{(x - 1)^{2}})(0)}{(1)})){4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}ln^{3}(1)ln(4)}{(x - 1)^{9}} - \frac{8 * {1}^{\frac{1}{(x - 1)^{2}}}({4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}((({1}^{\frac{1}{(x - 1)^{2}}}(((\frac{-2(1 + 0)}{(x - 1)^{3}}))ln(1) + \frac{(\frac{1}{(x - 1)^{2}})(0)}{(1)})) + 0)ln(4) + \frac{({1}^{\frac{1}{(x - 1)^{2}}} + 4)(0)}{(4)}))ln^{3}(1)ln(4)}{(x - 1)^{9}} - \frac{8 * {1}^{\frac{1}{(x - 1)^{2}}}{4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}*3ln^{2}(1)*0ln(4)}{(x - 1)^{9}(1)} - \frac{8 * {1}^{\frac{1}{(x - 1)^{2}}}{4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}ln^{3}(1)*0}{(x - 1)^{9}(4)} - 8(\frac{-9(1 + 0)}{(x - 1)^{10}}){1}^{(2(\frac{1}{(x - 1)^{2}}))}{4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}ln^{3}(1)ln^{2}(4) - \frac{8({1}^{(2(\frac{1}{(x - 1)^{2}}))}((2((\frac{-2(1 + 0)}{(x - 1)^{3}})))ln(1) + \frac{(2(\frac{1}{(x - 1)^{2}}))(0)}{(1)})){4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}ln^{3}(1)ln^{2}(4)}{(x - 1)^{9}} - \frac{8 * {1}^{(2(\frac{1}{(x - 1)^{2}}))}({4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}((({1}^{\frac{1}{(x - 1)^{2}}}(((\frac{-2(1 + 0)}{(x - 1)^{3}}))ln(1) + \frac{(\frac{1}{(x - 1)^{2}})(0)}{(1)})) + 0)ln(4) + \frac{({1}^{\frac{1}{(x - 1)^{2}}} + 4)(0)}{(4)}))ln^{3}(1)ln^{2}(4)}{(x - 1)^{9}} - \frac{8 * {1}^{(2(\frac{1}{(x - 1)^{2}}))}{4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}*3ln^{2}(1)*0ln^{2}(4)}{(x - 1)^{9}(1)} - \frac{8 * {1}^{(2(\frac{1}{(x - 1)^{2}}))}{4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}ln^{3}(1)*2ln(4)*0}{(x - 1)^{9}(4)} - 24(\frac{-7(1 + 0)}{(x - 1)^{8}}){1}^{(\frac{2}{(x - 1)^{2}})}{4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}ln^{2}(1)ln^{2}(4) - \frac{24({1}^{(\frac{2}{(x - 1)^{2}})}((2(\frac{-2(1 + 0)}{(x - 1)^{3}}))ln(1) + \frac{(\frac{2}{(x - 1)^{2}})(0)}{(1)})){4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}ln^{2}(1)ln^{2}(4)}{(x - 1)^{7}} - \frac{24 * {1}^{(\frac{2}{(x - 1)^{2}})}({4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}((({1}^{\frac{1}{(x - 1)^{2}}}(((\frac{-2(1 + 0)}{(x - 1)^{3}}))ln(1) + \frac{(\frac{1}{(x - 1)^{2}})(0)}{(1)})) + 0)ln(4) + \frac{({1}^{\frac{1}{(x - 1)^{2}}} + 4)(0)}{(4)}))ln^{2}(1)ln^{2}(4)}{(x - 1)^{7}} - \frac{24 * {1}^{(\frac{2}{(x - 1)^{2}})}{4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}*2ln(1)*0ln^{2}(4)}{(x - 1)^{7}(1)} - \frac{24 * {1}^{(\frac{2}{(x - 1)^{2}})}{4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}ln^{2}(1)*2ln(4)*0}{(x - 1)^{7}(4)} - 16(\frac{-9(1 + 0)}{(x - 1)^{10}}){1}^{(\frac{2}{(x - 1)^{2}})}{4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}ln^{3}(1)ln^{2}(4) - \frac{16({1}^{(\frac{2}{(x - 1)^{2}})}((2(\frac{-2(1 + 0)}{(x - 1)^{3}}))ln(1) + \frac{(\frac{2}{(x - 1)^{2}})(0)}{(1)})){4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}ln^{3}(1)ln^{2}(4)}{(x - 1)^{9}} - \frac{16 * {1}^{(\frac{2}{(x - 1)^{2}})}({4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}((({1}^{\frac{1}{(x - 1)^{2}}}(((\frac{-2(1 + 0)}{(x - 1)^{3}}))ln(1) + \frac{(\frac{1}{(x - 1)^{2}})(0)}{(1)})) + 0)ln(4) + \frac{({1}^{\frac{1}{(x - 1)^{2}}} + 4)(0)}{(4)}))ln^{3}(1)ln^{2}(4)}{(x - 1)^{9}} - \frac{16 * {1}^{(\frac{2}{(x - 1)^{2}})}{4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}*3ln^{2}(1)*0ln^{2}(4)}{(x - 1)^{9}(1)} - \frac{16 * {1}^{(\frac{2}{(x - 1)^{2}})}{4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}ln^{3}(1)*2ln(4)*0}{(x - 1)^{9}(4)} - 8(\frac{-9(1 + 0)}{(x - 1)^{10}}){1}^{(\frac{3}{(x - 1)^{2}})}{4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}ln^{3}(1)ln^{3}(4) - \frac{8({1}^{(\frac{3}{(x - 1)^{2}})}((3(\frac{-2(1 + 0)}{(x - 1)^{3}}))ln(1) + \frac{(\frac{3}{(x - 1)^{2}})(0)}{(1)})){4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}ln^{3}(1)ln^{3}(4)}{(x - 1)^{9}} - \frac{8 * {1}^{(\frac{3}{(x - 1)^{2}})}({4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}((({1}^{\frac{1}{(x - 1)^{2}}}(((\frac{-2(1 + 0)}{(x - 1)^{3}}))ln(1) + \frac{(\frac{1}{(x - 1)^{2}})(0)}{(1)})) + 0)ln(4) + \frac{({1}^{\frac{1}{(x - 1)^{2}}} + 4)(0)}{(4)}))ln^{3}(1)ln^{3}(4)}{(x - 1)^{9}} - \frac{8 * {1}^{(\frac{3}{(x - 1)^{2}})}{4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}*3ln^{2}(1)*0ln^{3}(4)}{(x - 1)^{9}(1)} - \frac{8 * {1}^{(\frac{3}{(x - 1)^{2}})}{4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}ln^{3}(1)*3ln^{2}(4)*0}{(x - 1)^{9}(4)}\\=&\frac{120 * {1}^{\frac{1}{(x - 1)^{2}}}{4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}ln(4)ln(1)}{(x - 1)^{6}} + \frac{300 * {1}^{\frac{1}{(x - 1)^{2}}}{4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}ln^{2}(1)ln(4)}{(x - 1)^{8}} + \frac{48 * {1}^{(2(\frac{1}{(x - 1)^{2}}))}{4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}ln^{2}(1)ln^{2}(4)}{(x - 1)^{8}} + \frac{144 * {1}^{\frac{1}{(x - 1)^{2}}}{4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}ln^{3}(1)ln(4)}{(x - 1)^{10}} + \frac{72 * {1}^{(2(\frac{1}{(x - 1)^{2}}))}{4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}ln^{3}(1)ln^{2}(4)}{(x - 1)^{10}} + \frac{252 * {1}^{(\frac{2}{(x - 1)^{2}})}{4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}ln^{2}(1)ln^{2}(4)}{(x - 1)^{8}} + \frac{360 * {1}^{(\frac{2}{(x - 1)^{2}})}{4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}ln^{3}(1)ln^{2}(4)}{(x - 1)^{10}} + \frac{144 * {1}^{(\frac{3}{(x - 1)^{2}})}{4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}ln^{3}(1)ln^{3}(4)}{(x - 1)^{10}} + \frac{16 * {1}^{\frac{1}{(x - 1)^{2}}}{4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}ln^{4}(1)ln(4)}{(x - 1)^{12}} + \frac{16 * {1}^{(2(\frac{1}{(x - 1)^{2}}))}{4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}ln^{4}(1)ln^{2}(4)}{(x - 1)^{12}} + \frac{96 * {1}^{(\frac{2}{(x - 1)^{2}})}{4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}ln^{4}(1)ln^{2}(4)}{(x - 1)^{12}} + \frac{96 * {1}^{(\frac{3}{(x - 1)^{2}})}{4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}ln^{4}(1)ln^{3}(4)}{(x - 1)^{12}} + \frac{16 * {1}^{(\frac{4}{(x - 1)^{2}})}{4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}ln^{4}(1)ln^{4}(4)}{(x - 1)^{12}}\\ \end{split}\end{equation} \]
注意，变量是区分大小写的。
\[ \begin{equation}\begin{split}【1/1】求函数{4}^{(4 + {1}^{{(\frac{1}{(x - 1)})}^{2}})} 关于 x 的 4 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = {4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( {4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}\right)}{dx}\\=&({4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}((({1}^{\frac{1}{(x - 1)^{2}}}(((\frac{-2(1 + 0)}{(x - 1)^{3}}))ln(1) + \frac{(\frac{1}{(x - 1)^{2}})(0)}{(1)})) + 0)ln(4) + \frac{({1}^{\frac{1}{(x - 1)^{2}}} + 4)(0)}{(4)}))\\=&\frac{-2 * {1}^{\frac{1}{(x - 1)^{2}}}{4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}ln(4)ln(1)}{(x - 1)^{3}}\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( \frac{-2 * {1}^{\frac{1}{(x - 1)^{2}}}{4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}ln(4)ln(1)}{(x - 1)^{3}}\right)}{dx}\\=&-2(\frac{-3(1 + 0)}{(x - 1)^{4}}){1}^{\frac{1}{(x - 1)^{2}}}{4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}ln(4)ln(1) - \frac{2({1}^{\frac{1}{(x - 1)^{2}}}(((\frac{-2(1 + 0)}{(x - 1)^{3}}))ln(1) + \frac{(\frac{1}{(x - 1)^{2}})(0)}{(1)})){4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}ln(4)ln(1)}{(x - 1)^{3}} - \frac{2 * {1}^{\frac{1}{(x - 1)^{2}}}({4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}((({1}^{\frac{1}{(x - 1)^{2}}}(((\frac{-2(1 + 0)}{(x - 1)^{3}}))ln(1) + \frac{(\frac{1}{(x - 1)^{2}})(0)}{(1)})) + 0)ln(4) + \frac{({1}^{\frac{1}{(x - 1)^{2}}} + 4)(0)}{(4)}))ln(4)ln(1)}{(x - 1)^{3}} - \frac{2 * {1}^{\frac{1}{(x - 1)^{2}}}{4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}*0ln(1)}{(x - 1)^{3}(4)} - \frac{2 * {1}^{\frac{1}{(x - 1)^{2}}}{4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}ln(4)*0}{(x - 1)^{3}(1)}\\=&\frac{6 * {1}^{\frac{1}{(x - 1)^{2}}}{4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}ln(4)ln(1)}{(x - 1)^{4}} + \frac{4 * {1}^{\frac{1}{(x - 1)^{2}}}{4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}ln^{2}(1)ln(4)}{(x - 1)^{6}} + \frac{4 * {1}^{(2(\frac{1}{(x - 1)^{2}}))}{4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}ln^{2}(1)ln^{2}(4)}{(x - 1)^{6}}\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( \frac{6 * {1}^{\frac{1}{(x - 1)^{2}}}{4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}ln(4)ln(1)}{(x - 1)^{4}} + \frac{4 * {1}^{\frac{1}{(x - 1)^{2}}}{4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}ln^{2}(1)ln(4)}{(x - 1)^{6}} + \frac{4 * {1}^{(2(\frac{1}{(x - 1)^{2}}))}{4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}ln^{2}(1)ln^{2}(4)}{(x - 1)^{6}}\right)}{dx}\\=&6(\frac{-4(1 + 0)}{(x - 1)^{5}}){1}^{\frac{1}{(x - 1)^{2}}}{4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}ln(4)ln(1) + \frac{6({1}^{\frac{1}{(x - 1)^{2}}}(((\frac{-2(1 + 0)}{(x - 1)^{3}}))ln(1) + \frac{(\frac{1}{(x - 1)^{2}})(0)}{(1)})){4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}ln(4)ln(1)}{(x - 1)^{4}} + \frac{6 * {1}^{\frac{1}{(x - 1)^{2}}}({4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}((({1}^{\frac{1}{(x - 1)^{2}}}(((\frac{-2(1 + 0)}{(x - 1)^{3}}))ln(1) + \frac{(\frac{1}{(x - 1)^{2}})(0)}{(1)})) + 0)ln(4) + \frac{({1}^{\frac{1}{(x - 1)^{2}}} + 4)(0)}{(4)}))ln(4)ln(1)}{(x - 1)^{4}} + \frac{6 * {1}^{\frac{1}{(x - 1)^{2}}}{4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}*0ln(1)}{(x - 1)^{4}(4)} + \frac{6 * {1}^{\frac{1}{(x - 1)^{2}}}{4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}ln(4)*0}{(x - 1)^{4}(1)} + 4(\frac{-6(1 + 0)}{(x - 1)^{7}}){1}^{\frac{1}{(x - 1)^{2}}}{4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}ln^{2}(1)ln(4) + \frac{4({1}^{\frac{1}{(x - 1)^{2}}}(((\frac{-2(1 + 0)}{(x - 1)^{3}}))ln(1) + \frac{(\frac{1}{(x - 1)^{2}})(0)}{(1)})){4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}ln^{2}(1)ln(4)}{(x - 1)^{6}} + \frac{4 * {1}^{\frac{1}{(x - 1)^{2}}}({4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}((({1}^{\frac{1}{(x - 1)^{2}}}(((\frac{-2(1 + 0)}{(x - 1)^{3}}))ln(1) + \frac{(\frac{1}{(x - 1)^{2}})(0)}{(1)})) + 0)ln(4) + \frac{({1}^{\frac{1}{(x - 1)^{2}}} + 4)(0)}{(4)}))ln^{2}(1)ln(4)}{(x - 1)^{6}} + \frac{4 * {1}^{\frac{1}{(x - 1)^{2}}}{4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}*2ln(1)*0ln(4)}{(x - 1)^{6}(1)} + \frac{4 * {1}^{\frac{1}{(x - 1)^{2}}}{4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}ln^{2}(1)*0}{(x - 1)^{6}(4)} + 4(\frac{-6(1 + 0)}{(x - 1)^{7}}){1}^{(2(\frac{1}{(x - 1)^{2}}))}{4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}ln^{2}(1)ln^{2}(4) + \frac{4({1}^{(2(\frac{1}{(x - 1)^{2}}))}((2((\frac{-2(1 + 0)}{(x - 1)^{3}})))ln(1) + \frac{(2(\frac{1}{(x - 1)^{2}}))(0)}{(1)})){4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}ln^{2}(1)ln^{2}(4)}{(x - 1)^{6}} + \frac{4 * {1}^{(2(\frac{1}{(x - 1)^{2}}))}({4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}((({1}^{\frac{1}{(x - 1)^{2}}}(((\frac{-2(1 + 0)}{(x - 1)^{3}}))ln(1) + \frac{(\frac{1}{(x - 1)^{2}})(0)}{(1)})) + 0)ln(4) + \frac{({1}^{\frac{1}{(x - 1)^{2}}} + 4)(0)}{(4)}))ln^{2}(1)ln^{2}(4)}{(x - 1)^{6}} + \frac{4 * {1}^{(2(\frac{1}{(x - 1)^{2}}))}{4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}*2ln(1)*0ln^{2}(4)}{(x - 1)^{6}(1)} + \frac{4 * {1}^{(2(\frac{1}{(x - 1)^{2}}))}{4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}ln^{2}(1)*2ln(4)*0}{(x - 1)^{6}(4)}\\=&\frac{-24 * {1}^{\frac{1}{(x - 1)^{2}}}{4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}ln(4)ln(1)}{(x - 1)^{5}} - \frac{36 * {1}^{\frac{1}{(x - 1)^{2}}}{4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}ln^{2}(1)ln(4)}{(x - 1)^{7}} - \frac{12 * {1}^{(2(\frac{1}{(x - 1)^{2}}))}{4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}ln^{2}(1)ln^{2}(4)}{(x - 1)^{7}} - \frac{8 * {1}^{\frac{1}{(x - 1)^{2}}}{4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}ln^{3}(1)ln(4)}{(x - 1)^{9}} - \frac{8 * {1}^{(2(\frac{1}{(x - 1)^{2}}))}{4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}ln^{3}(1)ln^{2}(4)}{(x - 1)^{9}} - \frac{24 * {1}^{(\frac{2}{(x - 1)^{2}})}{4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}ln^{2}(1)ln^{2}(4)}{(x - 1)^{7}} - \frac{16 * {1}^{(\frac{2}{(x - 1)^{2}})}{4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}ln^{3}(1)ln^{2}(4)}{(x - 1)^{9}} - \frac{8 * {1}^{(\frac{3}{(x - 1)^{2}})}{4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}ln^{3}(1)ln^{3}(4)}{(x - 1)^{9}}\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( \frac{-24 * {1}^{\frac{1}{(x - 1)^{2}}}{4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}ln(4)ln(1)}{(x - 1)^{5}} - \frac{36 * {1}^{\frac{1}{(x - 1)^{2}}}{4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}ln^{2}(1)ln(4)}{(x - 1)^{7}} - \frac{12 * {1}^{(2(\frac{1}{(x - 1)^{2}}))}{4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}ln^{2}(1)ln^{2}(4)}{(x - 1)^{7}} - \frac{8 * {1}^{\frac{1}{(x - 1)^{2}}}{4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}ln^{3}(1)ln(4)}{(x - 1)^{9}} - \frac{8 * {1}^{(2(\frac{1}{(x - 1)^{2}}))}{4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}ln^{3}(1)ln^{2}(4)}{(x - 1)^{9}} - \frac{24 * {1}^{(\frac{2}{(x - 1)^{2}})}{4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}ln^{2}(1)ln^{2}(4)}{(x - 1)^{7}} - \frac{16 * {1}^{(\frac{2}{(x - 1)^{2}})}{4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}ln^{3}(1)ln^{2}(4)}{(x - 1)^{9}} - \frac{8 * {1}^{(\frac{3}{(x - 1)^{2}})}{4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}ln^{3}(1)ln^{3}(4)}{(x - 1)^{9}}\right)}{dx}\\=&-24(\frac{-5(1 + 0)}{(x - 1)^{6}}){1}^{\frac{1}{(x - 1)^{2}}}{4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}ln(4)ln(1) - \frac{24({1}^{\frac{1}{(x - 1)^{2}}}(((\frac{-2(1 + 0)}{(x - 1)^{3}}))ln(1) + \frac{(\frac{1}{(x - 1)^{2}})(0)}{(1)})){4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}ln(4)ln(1)}{(x - 1)^{5}} - \frac{24 * {1}^{\frac{1}{(x - 1)^{2}}}({4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}((({1}^{\frac{1}{(x - 1)^{2}}}(((\frac{-2(1 + 0)}{(x - 1)^{3}}))ln(1) + \frac{(\frac{1}{(x - 1)^{2}})(0)}{(1)})) + 0)ln(4) + \frac{({1}^{\frac{1}{(x - 1)^{2}}} + 4)(0)}{(4)}))ln(4)ln(1)}{(x - 1)^{5}} - \frac{24 * {1}^{\frac{1}{(x - 1)^{2}}}{4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}*0ln(1)}{(x - 1)^{5}(4)} - \frac{24 * {1}^{\frac{1}{(x - 1)^{2}}}{4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}ln(4)*0}{(x - 1)^{5}(1)} - 36(\frac{-7(1 + 0)}{(x - 1)^{8}}){1}^{\frac{1}{(x - 1)^{2}}}{4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}ln^{2}(1)ln(4) - \frac{36({1}^{\frac{1}{(x - 1)^{2}}}(((\frac{-2(1 + 0)}{(x - 1)^{3}}))ln(1) + \frac{(\frac{1}{(x - 1)^{2}})(0)}{(1)})){4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}ln^{2}(1)ln(4)}{(x - 1)^{7}} - \frac{36 * {1}^{\frac{1}{(x - 1)^{2}}}({4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}((({1}^{\frac{1}{(x - 1)^{2}}}(((\frac{-2(1 + 0)}{(x - 1)^{3}}))ln(1) + \frac{(\frac{1}{(x - 1)^{2}})(0)}{(1)})) + 0)ln(4) + \frac{({1}^{\frac{1}{(x - 1)^{2}}} + 4)(0)}{(4)}))ln^{2}(1)ln(4)}{(x - 1)^{7}} - \frac{36 * {1}^{\frac{1}{(x - 1)^{2}}}{4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}*2ln(1)*0ln(4)}{(x - 1)^{7}(1)} - \frac{36 * {1}^{\frac{1}{(x - 1)^{2}}}{4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}ln^{2}(1)*0}{(x - 1)^{7}(4)} - 12(\frac{-7(1 + 0)}{(x - 1)^{8}}){1}^{(2(\frac{1}{(x - 1)^{2}}))}{4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}ln^{2}(1)ln^{2}(4) - \frac{12({1}^{(2(\frac{1}{(x - 1)^{2}}))}((2((\frac{-2(1 + 0)}{(x - 1)^{3}})))ln(1) + \frac{(2(\frac{1}{(x - 1)^{2}}))(0)}{(1)})){4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}ln^{2}(1)ln^{2}(4)}{(x - 1)^{7}} - \frac{12 * {1}^{(2(\frac{1}{(x - 1)^{2}}))}({4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}((({1}^{\frac{1}{(x - 1)^{2}}}(((\frac{-2(1 + 0)}{(x - 1)^{3}}))ln(1) + \frac{(\frac{1}{(x - 1)^{2}})(0)}{(1)})) + 0)ln(4) + \frac{({1}^{\frac{1}{(x - 1)^{2}}} + 4)(0)}{(4)}))ln^{2}(1)ln^{2}(4)}{(x - 1)^{7}} - \frac{12 * {1}^{(2(\frac{1}{(x - 1)^{2}}))}{4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}*2ln(1)*0ln^{2}(4)}{(x - 1)^{7}(1)} - \frac{12 * {1}^{(2(\frac{1}{(x - 1)^{2}}))}{4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}ln^{2}(1)*2ln(4)*0}{(x - 1)^{7}(4)} - 8(\frac{-9(1 + 0)}{(x - 1)^{10}}){1}^{\frac{1}{(x - 1)^{2}}}{4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}ln^{3}(1)ln(4) - \frac{8({1}^{\frac{1}{(x - 1)^{2}}}(((\frac{-2(1 + 0)}{(x - 1)^{3}}))ln(1) + \frac{(\frac{1}{(x - 1)^{2}})(0)}{(1)})){4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}ln^{3}(1)ln(4)}{(x - 1)^{9}} - \frac{8 * {1}^{\frac{1}{(x - 1)^{2}}}({4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}((({1}^{\frac{1}{(x - 1)^{2}}}(((\frac{-2(1 + 0)}{(x - 1)^{3}}))ln(1) + \frac{(\frac{1}{(x - 1)^{2}})(0)}{(1)})) + 0)ln(4) + \frac{({1}^{\frac{1}{(x - 1)^{2}}} + 4)(0)}{(4)}))ln^{3}(1)ln(4)}{(x - 1)^{9}} - \frac{8 * {1}^{\frac{1}{(x - 1)^{2}}}{4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}*3ln^{2}(1)*0ln(4)}{(x - 1)^{9}(1)} - \frac{8 * {1}^{\frac{1}{(x - 1)^{2}}}{4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}ln^{3}(1)*0}{(x - 1)^{9}(4)} - 8(\frac{-9(1 + 0)}{(x - 1)^{10}}){1}^{(2(\frac{1}{(x - 1)^{2}}))}{4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}ln^{3}(1)ln^{2}(4) - \frac{8({1}^{(2(\frac{1}{(x - 1)^{2}}))}((2((\frac{-2(1 + 0)}{(x - 1)^{3}})))ln(1) + \frac{(2(\frac{1}{(x - 1)^{2}}))(0)}{(1)})){4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}ln^{3}(1)ln^{2}(4)}{(x - 1)^{9}} - \frac{8 * {1}^{(2(\frac{1}{(x - 1)^{2}}))}({4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}((({1}^{\frac{1}{(x - 1)^{2}}}(((\frac{-2(1 + 0)}{(x - 1)^{3}}))ln(1) + \frac{(\frac{1}{(x - 1)^{2}})(0)}{(1)})) + 0)ln(4) + \frac{({1}^{\frac{1}{(x - 1)^{2}}} + 4)(0)}{(4)}))ln^{3}(1)ln^{2}(4)}{(x - 1)^{9}} - \frac{8 * {1}^{(2(\frac{1}{(x - 1)^{2}}))}{4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}*3ln^{2}(1)*0ln^{2}(4)}{(x - 1)^{9}(1)} - \frac{8 * {1}^{(2(\frac{1}{(x - 1)^{2}}))}{4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}ln^{3}(1)*2ln(4)*0}{(x - 1)^{9}(4)} - 24(\frac{-7(1 + 0)}{(x - 1)^{8}}){1}^{(\frac{2}{(x - 1)^{2}})}{4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}ln^{2}(1)ln^{2}(4) - \frac{24({1}^{(\frac{2}{(x - 1)^{2}})}((2(\frac{-2(1 + 0)}{(x - 1)^{3}}))ln(1) + \frac{(\frac{2}{(x - 1)^{2}})(0)}{(1)})){4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}ln^{2}(1)ln^{2}(4)}{(x - 1)^{7}} - \frac{24 * {1}^{(\frac{2}{(x - 1)^{2}})}({4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}((({1}^{\frac{1}{(x - 1)^{2}}}(((\frac{-2(1 + 0)}{(x - 1)^{3}}))ln(1) + \frac{(\frac{1}{(x - 1)^{2}})(0)}{(1)})) + 0)ln(4) + \frac{({1}^{\frac{1}{(x - 1)^{2}}} + 4)(0)}{(4)}))ln^{2}(1)ln^{2}(4)}{(x - 1)^{7}} - \frac{24 * {1}^{(\frac{2}{(x - 1)^{2}})}{4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}*2ln(1)*0ln^{2}(4)}{(x - 1)^{7}(1)} - \frac{24 * {1}^{(\frac{2}{(x - 1)^{2}})}{4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}ln^{2}(1)*2ln(4)*0}{(x - 1)^{7}(4)} - 16(\frac{-9(1 + 0)}{(x - 1)^{10}}){1}^{(\frac{2}{(x - 1)^{2}})}{4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}ln^{3}(1)ln^{2}(4) - \frac{16({1}^{(\frac{2}{(x - 1)^{2}})}((2(\frac{-2(1 + 0)}{(x - 1)^{3}}))ln(1) + \frac{(\frac{2}{(x - 1)^{2}})(0)}{(1)})){4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}ln^{3}(1)ln^{2}(4)}{(x - 1)^{9}} - \frac{16 * {1}^{(\frac{2}{(x - 1)^{2}})}({4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}((({1}^{\frac{1}{(x - 1)^{2}}}(((\frac{-2(1 + 0)}{(x - 1)^{3}}))ln(1) + \frac{(\frac{1}{(x - 1)^{2}})(0)}{(1)})) + 0)ln(4) + \frac{({1}^{\frac{1}{(x - 1)^{2}}} + 4)(0)}{(4)}))ln^{3}(1)ln^{2}(4)}{(x - 1)^{9}} - \frac{16 * {1}^{(\frac{2}{(x - 1)^{2}})}{4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}*3ln^{2}(1)*0ln^{2}(4)}{(x - 1)^{9}(1)} - \frac{16 * {1}^{(\frac{2}{(x - 1)^{2}})}{4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}ln^{3}(1)*2ln(4)*0}{(x - 1)^{9}(4)} - 8(\frac{-9(1 + 0)}{(x - 1)^{10}}){1}^{(\frac{3}{(x - 1)^{2}})}{4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}ln^{3}(1)ln^{3}(4) - \frac{8({1}^{(\frac{3}{(x - 1)^{2}})}((3(\frac{-2(1 + 0)}{(x - 1)^{3}}))ln(1) + \frac{(\frac{3}{(x - 1)^{2}})(0)}{(1)})){4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}ln^{3}(1)ln^{3}(4)}{(x - 1)^{9}} - \frac{8 * {1}^{(\frac{3}{(x - 1)^{2}})}({4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}((({1}^{\frac{1}{(x - 1)^{2}}}(((\frac{-2(1 + 0)}{(x - 1)^{3}}))ln(1) + \frac{(\frac{1}{(x - 1)^{2}})(0)}{(1)})) + 0)ln(4) + \frac{({1}^{\frac{1}{(x - 1)^{2}}} + 4)(0)}{(4)}))ln^{3}(1)ln^{3}(4)}{(x - 1)^{9}} - \frac{8 * {1}^{(\frac{3}{(x - 1)^{2}})}{4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}*3ln^{2}(1)*0ln^{3}(4)}{(x - 1)^{9}(1)} - \frac{8 * {1}^{(\frac{3}{(x - 1)^{2}})}{4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}ln^{3}(1)*3ln^{2}(4)*0}{(x - 1)^{9}(4)}\\=&\frac{120 * {1}^{\frac{1}{(x - 1)^{2}}}{4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}ln(4)ln(1)}{(x - 1)^{6}} + \frac{300 * {1}^{\frac{1}{(x - 1)^{2}}}{4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}ln^{2}(1)ln(4)}{(x - 1)^{8}} + \frac{48 * {1}^{(2(\frac{1}{(x - 1)^{2}}))}{4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}ln^{2}(1)ln^{2}(4)}{(x - 1)^{8}} + \frac{144 * {1}^{\frac{1}{(x - 1)^{2}}}{4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}ln^{3}(1)ln(4)}{(x - 1)^{10}} + \frac{72 * {1}^{(2(\frac{1}{(x - 1)^{2}}))}{4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}ln^{3}(1)ln^{2}(4)}{(x - 1)^{10}} + \frac{252 * {1}^{(\frac{2}{(x - 1)^{2}})}{4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}ln^{2}(1)ln^{2}(4)}{(x - 1)^{8}} + \frac{360 * {1}^{(\frac{2}{(x - 1)^{2}})}{4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}ln^{3}(1)ln^{2}(4)}{(x - 1)^{10}} + \frac{144 * {1}^{(\frac{3}{(x - 1)^{2}})}{4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}ln^{3}(1)ln^{3}(4)}{(x - 1)^{10}} + \frac{16 * {1}^{\frac{1}{(x - 1)^{2}}}{4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}ln^{4}(1)ln(4)}{(x - 1)^{12}} + \frac{16 * {1}^{(2(\frac{1}{(x - 1)^{2}}))}{4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}ln^{4}(1)ln^{2}(4)}{(x - 1)^{12}} + \frac{96 * {1}^{(\frac{2}{(x - 1)^{2}})}{4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}ln^{4}(1)ln^{2}(4)}{(x - 1)^{12}} + \frac{96 * {1}^{(\frac{3}{(x - 1)^{2}})}{4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}ln^{4}(1)ln^{3}(4)}{(x - 1)^{12}} + \frac{16 * {1}^{(\frac{4}{(x - 1)^{2}})}{4}^{({1}^{\frac{1}{(x - 1)^{2}}} + 4)}ln^{4}(1)ln^{4}(4)}{(x - 1)^{12}}\\ \end{split}\end{equation} \]
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