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。
\[ \begin{equation}\begin{split}【1/1】求函数{({x}^{2} - 3x + 2)}^{n}cos(\frac{pi{x}^{2}}{12}) 关于 x 的 4 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = (x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( (x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})\right)}{dx}\\=&((x^{2} - 3x + 2)^{n}((0)ln(x^{2} - 3x + 2) + \frac{(n)(2x - 3 + 0)}{(x^{2} - 3x + 2)}))cos(\frac{1}{12}pix^{2}) + (x^{2} - 3x + 2)^{n}*-sin(\frac{1}{12}pix^{2})*\frac{1}{12}pi*2x\\=&\frac{2nx(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)} - \frac{3n(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)} - \frac{pix(x^{2} - 3x + 2)^{n}sin(\frac{1}{12}pix^{2})}{6}\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( \frac{2nx(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)} - \frac{3n(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)} - \frac{pix(x^{2} - 3x + 2)^{n}sin(\frac{1}{12}pix^{2})}{6}\right)}{dx}\\=&2(\frac{-(2x - 3 + 0)}{(x^{2} - 3x + 2)^{2}})nx(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2}) + \frac{2n(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)} + \frac{2nx((x^{2} - 3x + 2)^{n}((0)ln(x^{2} - 3x + 2) + \frac{(n)(2x - 3 + 0)}{(x^{2} - 3x + 2)}))cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)} + \frac{2nx(x^{2} - 3x + 2)^{n}*-sin(\frac{1}{12}pix^{2})*\frac{1}{12}pi*2x}{(x^{2} - 3x + 2)} - 3(\frac{-(2x - 3 + 0)}{(x^{2} - 3x + 2)^{2}})n(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2}) - \frac{3n((x^{2} - 3x + 2)^{n}((0)ln(x^{2} - 3x + 2) + \frac{(n)(2x - 3 + 0)}{(x^{2} - 3x + 2)}))cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)} - \frac{3n(x^{2} - 3x + 2)^{n}*-sin(\frac{1}{12}pix^{2})*\frac{1}{12}pi*2x}{(x^{2} - 3x + 2)} - \frac{pi(x^{2} - 3x + 2)^{n}sin(\frac{1}{12}pix^{2})}{6} - \frac{pix((x^{2} - 3x + 2)^{n}((0)ln(x^{2} - 3x + 2) + \frac{(n)(2x - 3 + 0)}{(x^{2} - 3x + 2)}))sin(\frac{1}{12}pix^{2})}{6} - \frac{pix(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})*\frac{1}{12}pi*2x}{6}\\=&\frac{-4nx^{2}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{2}} + \frac{12nx(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{2}} + \frac{2n(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)} + \frac{4n^{2}x^{2}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{2}} - \frac{12n^{2}x(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{2}} - \frac{2npix^{2}(x^{2} - 3x + 2)^{n}sin(\frac{1}{12}pix^{2})}{3(x^{2} - 3x + 2)} - \frac{9n(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{2}} + \frac{9n^{2}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{2}} + \frac{npix(x^{2} - 3x + 2)^{n}sin(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)} - \frac{pi(x^{2} - 3x + 2)^{n}sin(\frac{1}{12}pix^{2})}{6} - \frac{p^{2}i^{2}x^{2}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{36}\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( \frac{-4nx^{2}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{2}} + \frac{12nx(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{2}} + \frac{2n(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)} + \frac{4n^{2}x^{2}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{2}} - \frac{12n^{2}x(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{2}} - \frac{2npix^{2}(x^{2} - 3x + 2)^{n}sin(\frac{1}{12}pix^{2})}{3(x^{2} - 3x + 2)} - \frac{9n(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{2}} + \frac{9n^{2}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{2}} + \frac{npix(x^{2} - 3x + 2)^{n}sin(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)} - \frac{pi(x^{2} - 3x + 2)^{n}sin(\frac{1}{12}pix^{2})}{6} - \frac{p^{2}i^{2}x^{2}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{36}\right)}{dx}\\=&-4(\frac{-2(2x - 3 + 0)}{(x^{2} - 3x + 2)^{3}})nx^{2}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2}) - \frac{4n*2x(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{2}} - \frac{4nx^{2}((x^{2} - 3x + 2)^{n}((0)ln(x^{2} - 3x + 2) + \frac{(n)(2x - 3 + 0)}{(x^{2} - 3x + 2)}))cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{2}} - \frac{4nx^{2}(x^{2} - 3x + 2)^{n}*-sin(\frac{1}{12}pix^{2})*\frac{1}{12}pi*2x}{(x^{2} - 3x + 2)^{2}} + 12(\frac{-2(2x - 3 + 0)}{(x^{2} - 3x + 2)^{3}})nx(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2}) + \frac{12n(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{2}} + \frac{12nx((x^{2} - 3x + 2)^{n}((0)ln(x^{2} - 3x + 2) + \frac{(n)(2x - 3 + 0)}{(x^{2} - 3x + 2)}))cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{2}} + \frac{12nx(x^{2} - 3x + 2)^{n}*-sin(\frac{1}{12}pix^{2})*\frac{1}{12}pi*2x}{(x^{2} - 3x + 2)^{2}} + 2(\frac{-(2x - 3 + 0)}{(x^{2} - 3x + 2)^{2}})n(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2}) + \frac{2n((x^{2} - 3x + 2)^{n}((0)ln(x^{2} - 3x + 2) + \frac{(n)(2x - 3 + 0)}{(x^{2} - 3x + 2)}))cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)} + \frac{2n(x^{2} - 3x + 2)^{n}*-sin(\frac{1}{12}pix^{2})*\frac{1}{12}pi*2x}{(x^{2} - 3x + 2)} + 4(\frac{-2(2x - 3 + 0)}{(x^{2} - 3x + 2)^{3}})n^{2}x^{2}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2}) + \frac{4n^{2}*2x(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{2}} + \frac{4n^{2}x^{2}((x^{2} - 3x + 2)^{n}((0)ln(x^{2} - 3x + 2) + \frac{(n)(2x - 3 + 0)}{(x^{2} - 3x + 2)}))cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{2}} + \frac{4n^{2}x^{2}(x^{2} - 3x + 2)^{n}*-sin(\frac{1}{12}pix^{2})*\frac{1}{12}pi*2x}{(x^{2} - 3x + 2)^{2}} - 12(\frac{-2(2x - 3 + 0)}{(x^{2} - 3x + 2)^{3}})n^{2}x(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2}) - \frac{12n^{2}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{2}} - \frac{12n^{2}x((x^{2} - 3x + 2)^{n}((0)ln(x^{2} - 3x + 2) + \frac{(n)(2x - 3 + 0)}{(x^{2} - 3x + 2)}))cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{2}} - \frac{12n^{2}x(x^{2} - 3x + 2)^{n}*-sin(\frac{1}{12}pix^{2})*\frac{1}{12}pi*2x}{(x^{2} - 3x + 2)^{2}} - \frac{2(\frac{-(2x - 3 + 0)}{(x^{2} - 3x + 2)^{2}})npix^{2}(x^{2} - 3x + 2)^{n}sin(\frac{1}{12}pix^{2})}{3} - \frac{2npi*2x(x^{2} - 3x + 2)^{n}sin(\frac{1}{12}pix^{2})}{3(x^{2} - 3x + 2)} - \frac{2npix^{2}((x^{2} - 3x + 2)^{n}((0)ln(x^{2} - 3x + 2) + \frac{(n)(2x - 3 + 0)}{(x^{2} - 3x + 2)}))sin(\frac{1}{12}pix^{2})}{3(x^{2} - 3x + 2)} - \frac{2npix^{2}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})*\frac{1}{12}pi*2x}{3(x^{2} - 3x + 2)} - 9(\frac{-2(2x - 3 + 0)}{(x^{2} - 3x + 2)^{3}})n(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2}) - \frac{9n((x^{2} - 3x + 2)^{n}((0)ln(x^{2} - 3x + 2) + \frac{(n)(2x - 3 + 0)}{(x^{2} - 3x + 2)}))cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{2}} - \frac{9n(x^{2} - 3x + 2)^{n}*-sin(\frac{1}{12}pix^{2})*\frac{1}{12}pi*2x}{(x^{2} - 3x + 2)^{2}} + 9(\frac{-2(2x - 3 + 0)}{(x^{2} - 3x + 2)^{3}})n^{2}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2}) + \frac{9n^{2}((x^{2} - 3x + 2)^{n}((0)ln(x^{2} - 3x + 2) + \frac{(n)(2x - 3 + 0)}{(x^{2} - 3x + 2)}))cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{2}} + \frac{9n^{2}(x^{2} - 3x + 2)^{n}*-sin(\frac{1}{12}pix^{2})*\frac{1}{12}pi*2x}{(x^{2} - 3x + 2)^{2}} + (\frac{-(2x - 3 + 0)}{(x^{2} - 3x + 2)^{2}})npix(x^{2} - 3x + 2)^{n}sin(\frac{1}{12}pix^{2}) + \frac{npi(x^{2} - 3x + 2)^{n}sin(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)} + \frac{npix((x^{2} - 3x + 2)^{n}((0)ln(x^{2} - 3x + 2) + \frac{(n)(2x - 3 + 0)}{(x^{2} - 3x + 2)}))sin(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)} + \frac{npix(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})*\frac{1}{12}pi*2x}{(x^{2} - 3x + 2)} - \frac{pi((x^{2} - 3x + 2)^{n}((0)ln(x^{2} - 3x + 2) + \frac{(n)(2x - 3 + 0)}{(x^{2} - 3x + 2)}))sin(\frac{1}{12}pix^{2})}{6} - \frac{pi(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})*\frac{1}{12}pi*2x}{6} - \frac{p^{2}i^{2}*2x(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{36} - \frac{p^{2}i^{2}x^{2}((x^{2} - 3x + 2)^{n}((0)ln(x^{2} - 3x + 2) + \frac{(n)(2x - 3 + 0)}{(x^{2} - 3x + 2)}))cos(\frac{1}{12}pix^{2})}{36} - \frac{p^{2}i^{2}x^{2}(x^{2} - 3x + 2)^{n}*-sin(\frac{1}{12}pix^{2})*\frac{1}{12}pi*2x}{36}\\=&\frac{16nx^{3}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{3}} - \frac{72nx^{2}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{3}} - \frac{12nx(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{2}} - \frac{24n^{2}x^{3}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{3}} + \frac{108n^{2}x^{2}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{3}} + \frac{2npix^{3}(x^{2} - 3x + 2)^{n}sin(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{2}} + \frac{108nx(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{3}} + \frac{18n(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{2}} - \frac{162n^{2}x(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{3}} - \frac{6npix^{2}(x^{2} - 3x + 2)^{n}sin(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{2}} + \frac{12n^{2}x(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{2}} - \frac{18n^{2}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{2}} - \frac{2npix(x^{2} - 3x + 2)^{n}sin(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)} + \frac{8n^{3}x^{3}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{3}} - \frac{36n^{3}x^{2}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{3}} - \frac{2n^{2}pix^{3}(x^{2} - 3x + 2)^{n}sin(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{2}} + \frac{54n^{3}x(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{3}} + \frac{6n^{2}pix^{2}(x^{2} - 3x + 2)^{n}sin(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{2}} - \frac{np^{2}i^{2}x^{3}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{6(x^{2} - 3x + 2)} - \frac{54n(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{3}} + \frac{81n^{2}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{3}} + \frac{9npix(x^{2} - 3x + 2)^{n}sin(\frac{1}{12}pix^{2})}{2(x^{2} - 3x + 2)^{2}} - \frac{27n^{3}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{3}} - \frac{9n^{2}pix(x^{2} - 3x + 2)^{n}sin(\frac{1}{12}pix^{2})}{2(x^{2} - 3x + 2)^{2}} + \frac{3npi(x^{2} - 3x + 2)^{n}sin(\frac{1}{12}pix^{2})}{2(x^{2} - 3x + 2)} + \frac{np^{2}i^{2}x^{2}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{4(x^{2} - 3x + 2)} - \frac{p^{2}i^{2}x(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{12} + \frac{p^{3}i^{3}x^{3}(x^{2} - 3x + 2)^{n}sin(\frac{1}{12}pix^{2})}{216}\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( \frac{16nx^{3}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{3}} - \frac{72nx^{2}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{3}} - \frac{12nx(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{2}} - \frac{24n^{2}x^{3}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{3}} + \frac{108n^{2}x^{2}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{3}} + \frac{2npix^{3}(x^{2} - 3x + 2)^{n}sin(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{2}} + \frac{108nx(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{3}} + \frac{18n(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{2}} - \frac{162n^{2}x(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{3}} - \frac{6npix^{2}(x^{2} - 3x + 2)^{n}sin(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{2}} + \frac{12n^{2}x(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{2}} - \frac{18n^{2}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{2}} - \frac{2npix(x^{2} - 3x + 2)^{n}sin(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)} + \frac{8n^{3}x^{3}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{3}} - \frac{36n^{3}x^{2}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{3}} - \frac{2n^{2}pix^{3}(x^{2} - 3x + 2)^{n}sin(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{2}} + \frac{54n^{3}x(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{3}} + \frac{6n^{2}pix^{2}(x^{2} - 3x + 2)^{n}sin(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{2}} - \frac{np^{2}i^{2}x^{3}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{6(x^{2} - 3x + 2)} - \frac{54n(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{3}} + \frac{81n^{2}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{3}} + \frac{9npix(x^{2} - 3x + 2)^{n}sin(\frac{1}{12}pix^{2})}{2(x^{2} - 3x + 2)^{2}} - \frac{27n^{3}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{3}} - \frac{9n^{2}pix(x^{2} - 3x + 2)^{n}sin(\frac{1}{12}pix^{2})}{2(x^{2} - 3x + 2)^{2}} + \frac{3npi(x^{2} - 3x + 2)^{n}sin(\frac{1}{12}pix^{2})}{2(x^{2} - 3x + 2)} + \frac{np^{2}i^{2}x^{2}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{4(x^{2} - 3x + 2)} - \frac{p^{2}i^{2}x(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{12} + \frac{p^{3}i^{3}x^{3}(x^{2} - 3x + 2)^{n}sin(\frac{1}{12}pix^{2})}{216}\right)}{dx}\\=&16(\frac{-3(2x - 3 + 0)}{(x^{2} - 3x + 2)^{4}})nx^{3}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2}) + \frac{16n*3x^{2}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{3}} + \frac{16nx^{3}((x^{2} - 3x + 2)^{n}((0)ln(x^{2} - 3x + 2) + \frac{(n)(2x - 3 + 0)}{(x^{2} - 3x + 2)}))cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{3}} + \frac{16nx^{3}(x^{2} - 3x + 2)^{n}*-sin(\frac{1}{12}pix^{2})*\frac{1}{12}pi*2x}{(x^{2} - 3x + 2)^{3}} - 72(\frac{-3(2x - 3 + 0)}{(x^{2} - 3x + 2)^{4}})nx^{2}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2}) - \frac{72n*2x(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{3}} - \frac{72nx^{2}((x^{2} - 3x + 2)^{n}((0)ln(x^{2} - 3x + 2) + \frac{(n)(2x - 3 + 0)}{(x^{2} - 3x + 2)}))cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{3}} - \frac{72nx^{2}(x^{2} - 3x + 2)^{n}*-sin(\frac{1}{12}pix^{2})*\frac{1}{12}pi*2x}{(x^{2} - 3x + 2)^{3}} - 12(\frac{-2(2x - 3 + 0)}{(x^{2} - 3x + 2)^{3}})nx(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2}) - \frac{12n(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{2}} - \frac{12nx((x^{2} - 3x + 2)^{n}((0)ln(x^{2} - 3x + 2) + \frac{(n)(2x - 3 + 0)}{(x^{2} - 3x + 2)}))cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{2}} - \frac{12nx(x^{2} - 3x + 2)^{n}*-sin(\frac{1}{12}pix^{2})*\frac{1}{12}pi*2x}{(x^{2} - 3x + 2)^{2}} - 24(\frac{-3(2x - 3 + 0)}{(x^{2} - 3x + 2)^{4}})n^{2}x^{3}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2}) - \frac{24n^{2}*3x^{2}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{3}} - \frac{24n^{2}x^{3}((x^{2} - 3x + 2)^{n}((0)ln(x^{2} - 3x + 2) + \frac{(n)(2x - 3 + 0)}{(x^{2} - 3x + 2)}))cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{3}} - \frac{24n^{2}x^{3}(x^{2} - 3x + 2)^{n}*-sin(\frac{1}{12}pix^{2})*\frac{1}{12}pi*2x}{(x^{2} - 3x + 2)^{3}} + 108(\frac{-3(2x - 3 + 0)}{(x^{2} - 3x + 2)^{4}})n^{2}x^{2}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2}) + \frac{108n^{2}*2x(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{3}} + \frac{108n^{2}x^{2}((x^{2} - 3x + 2)^{n}((0)ln(x^{2} - 3x + 2) + \frac{(n)(2x - 3 + 0)}{(x^{2} - 3x + 2)}))cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{3}} + \frac{108n^{2}x^{2}(x^{2} - 3x + 2)^{n}*-sin(\frac{1}{12}pix^{2})*\frac{1}{12}pi*2x}{(x^{2} - 3x + 2)^{3}} + 2(\frac{-2(2x - 3 + 0)}{(x^{2} - 3x + 2)^{3}})npix^{3}(x^{2} - 3x + 2)^{n}sin(\frac{1}{12}pix^{2}) + \frac{2npi*3x^{2}(x^{2} - 3x + 2)^{n}sin(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{2}} + \frac{2npix^{3}((x^{2} - 3x + 2)^{n}((0)ln(x^{2} - 3x + 2) + \frac{(n)(2x - 3 + 0)}{(x^{2} - 3x + 2)}))sin(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{2}} + \frac{2npix^{3}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})*\frac{1}{12}pi*2x}{(x^{2} - 3x + 2)^{2}} + 108(\frac{-3(2x - 3 + 0)}{(x^{2} - 3x + 2)^{4}})nx(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2}) + \frac{108n(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{3}} + \frac{108nx((x^{2} - 3x + 2)^{n}((0)ln(x^{2} - 3x + 2) + \frac{(n)(2x - 3 + 0)}{(x^{2} - 3x + 2)}))cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{3}} + \frac{108nx(x^{2} - 3x + 2)^{n}*-sin(\frac{1}{12}pix^{2})*\frac{1}{12}pi*2x}{(x^{2} - 3x + 2)^{3}} + 18(\frac{-2(2x - 3 + 0)}{(x^{2} - 3x + 2)^{3}})n(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2}) + \frac{18n((x^{2} - 3x + 2)^{n}((0)ln(x^{2} - 3x + 2) + \frac{(n)(2x - 3 + 0)}{(x^{2} - 3x + 2)}))cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{2}} + \frac{18n(x^{2} - 3x + 2)^{n}*-sin(\frac{1}{12}pix^{2})*\frac{1}{12}pi*2x}{(x^{2} - 3x + 2)^{2}} - 162(\frac{-3(2x - 3 + 0)}{(x^{2} - 3x + 2)^{4}})n^{2}x(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2}) - \frac{162n^{2}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{3}} - \frac{162n^{2}x((x^{2} - 3x + 2)^{n}((0)ln(x^{2} - 3x + 2) + \frac{(n)(2x - 3 + 0)}{(x^{2} - 3x + 2)}))cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{3}} - \frac{162n^{2}x(x^{2} - 3x + 2)^{n}*-sin(\frac{1}{12}pix^{2})*\frac{1}{12}pi*2x}{(x^{2} - 3x + 2)^{3}} - 6(\frac{-2(2x - 3 + 0)}{(x^{2} - 3x + 2)^{3}})npix^{2}(x^{2} - 3x + 2)^{n}sin(\frac{1}{12}pix^{2}) - \frac{6npi*2x(x^{2} - 3x + 2)^{n}sin(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{2}} - \frac{6npix^{2}((x^{2} - 3x + 2)^{n}((0)ln(x^{2} - 3x + 2) + \frac{(n)(2x - 3 + 0)}{(x^{2} - 3x + 2)}))sin(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{2}} - \frac{6npix^{2}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})*\frac{1}{12}pi*2x}{(x^{2} - 3x + 2)^{2}} + 12(\frac{-2(2x - 3 + 0)}{(x^{2} - 3x + 2)^{3}})n^{2}x(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2}) + \frac{12n^{2}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{2}} + \frac{12n^{2}x((x^{2} - 3x + 2)^{n}((0)ln(x^{2} - 3x + 2) + \frac{(n)(2x - 3 + 0)}{(x^{2} - 3x + 2)}))cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{2}} + \frac{12n^{2}x(x^{2} - 3x + 2)^{n}*-sin(\frac{1}{12}pix^{2})*\frac{1}{12}pi*2x}{(x^{2} - 3x + 2)^{2}} - 18(\frac{-2(2x - 3 + 0)}{(x^{2} - 3x + 2)^{3}})n^{2}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2}) - \frac{18n^{2}((x^{2} - 3x + 2)^{n}((0)ln(x^{2} - 3x + 2) + \frac{(n)(2x - 3 + 0)}{(x^{2} - 3x + 2)}))cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{2}} - \frac{18n^{2}(x^{2} - 3x + 2)^{n}*-sin(\frac{1}{12}pix^{2})*\frac{1}{12}pi*2x}{(x^{2} - 3x + 2)^{2}} - 2(\frac{-(2x - 3 + 0)}{(x^{2} - 3x + 2)^{2}})npix(x^{2} - 3x + 2)^{n}sin(\frac{1}{12}pix^{2}) - \frac{2npi(x^{2} - 3x + 2)^{n}sin(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)} - \frac{2npix((x^{2} - 3x + 2)^{n}((0)ln(x^{2} - 3x + 2) + \frac{(n)(2x - 3 + 0)}{(x^{2} - 3x + 2)}))sin(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)} - \frac{2npix(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})*\frac{1}{12}pi*2x}{(x^{2} - 3x + 2)} + 8(\frac{-3(2x - 3 + 0)}{(x^{2} - 3x + 2)^{4}})n^{3}x^{3}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2}) + \frac{8n^{3}*3x^{2}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{3}} + \frac{8n^{3}x^{3}((x^{2} - 3x + 2)^{n}((0)ln(x^{2} - 3x + 2) + \frac{(n)(2x - 3 + 0)}{(x^{2} - 3x + 2)}))cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{3}} + \frac{8n^{3}x^{3}(x^{2} - 3x + 2)^{n}*-sin(\frac{1}{12}pix^{2})*\frac{1}{12}pi*2x}{(x^{2} - 3x + 2)^{3}} - 36(\frac{-3(2x - 3 + 0)}{(x^{2} - 3x + 2)^{4}})n^{3}x^{2}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2}) - \frac{36n^{3}*2x(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{3}} - \frac{36n^{3}x^{2}((x^{2} - 3x + 2)^{n}((0)ln(x^{2} - 3x + 2) + \frac{(n)(2x - 3 + 0)}{(x^{2} - 3x + 2)}))cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{3}} - \frac{36n^{3}x^{2}(x^{2} - 3x + 2)^{n}*-sin(\frac{1}{12}pix^{2})*\frac{1}{12}pi*2x}{(x^{2} - 3x + 2)^{3}} - 2(\frac{-2(2x - 3 + 0)}{(x^{2} - 3x + 2)^{3}})n^{2}pix^{3}(x^{2} - 3x + 2)^{n}sin(\frac{1}{12}pix^{2}) - \frac{2n^{2}pi*3x^{2}(x^{2} - 3x + 2)^{n}sin(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{2}} - \frac{2n^{2}pix^{3}((x^{2} - 3x + 2)^{n}((0)ln(x^{2} - 3x + 2) + \frac{(n)(2x - 3 + 0)}{(x^{2} - 3x + 2)}))sin(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{2}} - \frac{2n^{2}pix^{3}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})*\frac{1}{12}pi*2x}{(x^{2} - 3x + 2)^{2}} + 54(\frac{-3(2x - 3 + 0)}{(x^{2} - 3x + 2)^{4}})n^{3}x(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2}) + \frac{54n^{3}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{3}} + \frac{54n^{3}x((x^{2} - 3x + 2)^{n}((0)ln(x^{2} - 3x + 2) + \frac{(n)(2x - 3 + 0)}{(x^{2} - 3x + 2)}))cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{3}} + \frac{54n^{3}x(x^{2} - 3x + 2)^{n}*-sin(\frac{1}{12}pix^{2})*\frac{1}{12}pi*2x}{(x^{2} - 3x + 2)^{3}} + 6(\frac{-2(2x - 3 + 0)}{(x^{2} - 3x + 2)^{3}})n^{2}pix^{2}(x^{2} - 3x + 2)^{n}sin(\frac{1}{12}pix^{2}) + \frac{6n^{2}pi*2x(x^{2} - 3x + 2)^{n}sin(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{2}} + \frac{6n^{2}pix^{2}((x^{2} - 3x + 2)^{n}((0)ln(x^{2} - 3x + 2) + \frac{(n)(2x - 3 + 0)}{(x^{2} - 3x + 2)}))sin(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{2}} + \frac{6n^{2}pix^{2}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})*\frac{1}{12}pi*2x}{(x^{2} - 3x + 2)^{2}} - \frac{(\frac{-(2x - 3 + 0)}{(x^{2} - 3x + 2)^{2}})np^{2}i^{2}x^{3}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{6} - \frac{np^{2}i^{2}*3x^{2}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{6(x^{2} - 3x + 2)} - \frac{np^{2}i^{2}x^{3}((x^{2} - 3x + 2)^{n}((0)ln(x^{2} - 3x + 2) + \frac{(n)(2x - 3 + 0)}{(x^{2} - 3x + 2)}))cos(\frac{1}{12}pix^{2})}{6(x^{2} - 3x + 2)} - \frac{np^{2}i^{2}x^{3}(x^{2} - 3x + 2)^{n}*-sin(\frac{1}{12}pix^{2})*\frac{1}{12}pi*2x}{6(x^{2} - 3x + 2)} - 54(\frac{-3(2x - 3 + 0)}{(x^{2} - 3x + 2)^{4}})n(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2}) - \frac{54n((x^{2} - 3x + 2)^{n}((0)ln(x^{2} - 3x + 2) + \frac{(n)(2x - 3 + 0)}{(x^{2} - 3x + 2)}))cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{3}} - \frac{54n(x^{2} - 3x + 2)^{n}*-sin(\frac{1}{12}pix^{2})*\frac{1}{12}pi*2x}{(x^{2} - 3x + 2)^{3}} + 81(\frac{-3(2x - 3 + 0)}{(x^{2} - 3x + 2)^{4}})n^{2}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2}) + \frac{81n^{2}((x^{2} - 3x + 2)^{n}((0)ln(x^{2} - 3x + 2) + \frac{(n)(2x - 3 + 0)}{(x^{2} - 3x + 2)}))cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{3}} + \frac{81n^{2}(x^{2} - 3x + 2)^{n}*-sin(\frac{1}{12}pix^{2})*\frac{1}{12}pi*2x}{(x^{2} - 3x + 2)^{3}} + \frac{9(\frac{-2(2x - 3 + 0)}{(x^{2} - 3x + 2)^{3}})npix(x^{2} - 3x + 2)^{n}sin(\frac{1}{12}pix^{2})}{2} + \frac{9npi(x^{2} - 3x + 2)^{n}sin(\frac{1}{12}pix^{2})}{2(x^{2} - 3x + 2)^{2}} + \frac{9npix((x^{2} - 3x + 2)^{n}((0)ln(x^{2} - 3x + 2) + \frac{(n)(2x - 3 + 0)}{(x^{2} - 3x + 2)}))sin(\frac{1}{12}pix^{2})}{2(x^{2} - 3x + 2)^{2}} + \frac{9npix(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})*\frac{1}{12}pi*2x}{2(x^{2} - 3x + 2)^{2}} - 27(\frac{-3(2x - 3 + 0)}{(x^{2} - 3x + 2)^{4}})n^{3}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2}) - \frac{27n^{3}((x^{2} - 3x + 2)^{n}((0)ln(x^{2} - 3x + 2) + \frac{(n)(2x - 3 + 0)}{(x^{2} - 3x + 2)}))cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{3}} - \frac{27n^{3}(x^{2} - 3x + 2)^{n}*-sin(\frac{1}{12}pix^{2})*\frac{1}{12}pi*2x}{(x^{2} - 3x + 2)^{3}} - \frac{9(\frac{-2(2x - 3 + 0)}{(x^{2} - 3x + 2)^{3}})n^{2}pix(x^{2} - 3x + 2)^{n}sin(\frac{1}{12}pix^{2})}{2} - \frac{9n^{2}pi(x^{2} - 3x + 2)^{n}sin(\frac{1}{12}pix^{2})}{2(x^{2} - 3x + 2)^{2}} - \frac{9n^{2}pix((x^{2} - 3x + 2)^{n}((0)ln(x^{2} - 3x + 2) + \frac{(n)(2x - 3 + 0)}{(x^{2} - 3x + 2)}))sin(\frac{1}{12}pix^{2})}{2(x^{2} - 3x + 2)^{2}} - \frac{9n^{2}pix(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})*\frac{1}{12}pi*2x}{2(x^{2} - 3x + 2)^{2}} + \frac{3(\frac{-(2x - 3 + 0)}{(x^{2} - 3x + 2)^{2}})npi(x^{2} - 3x + 2)^{n}sin(\frac{1}{12}pix^{2})}{2} + \frac{3npi((x^{2} - 3x + 2)^{n}((0)ln(x^{2} - 3x + 2) + \frac{(n)(2x - 3 + 0)}{(x^{2} - 3x + 2)}))sin(\frac{1}{12}pix^{2})}{2(x^{2} - 3x + 2)} + \frac{3npi(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})*\frac{1}{12}pi*2x}{2(x^{2} - 3x + 2)} + \frac{(\frac{-(2x - 3 + 0)}{(x^{2} - 3x + 2)^{2}})np^{2}i^{2}x^{2}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{4} + \frac{np^{2}i^{2}*2x(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{4(x^{2} - 3x + 2)} + \frac{np^{2}i^{2}x^{2}((x^{2} - 3x + 2)^{n}((0)ln(x^{2} - 3x + 2) + \frac{(n)(2x - 3 + 0)}{(x^{2} - 3x + 2)}))cos(\frac{1}{12}pix^{2})}{4(x^{2} - 3x + 2)} + \frac{np^{2}i^{2}x^{2}(x^{2} - 3x + 2)^{n}*-sin(\frac{1}{12}pix^{2})*\frac{1}{12}pi*2x}{4(x^{2} - 3x + 2)} - \frac{p^{2}i^{2}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{12} - \frac{p^{2}i^{2}x((x^{2} - 3x + 2)^{n}((0)ln(x^{2} - 3x + 2) + \frac{(n)(2x - 3 + 0)}{(x^{2} - 3x + 2)}))cos(\frac{1}{12}pix^{2})}{12} - \frac{p^{2}i^{2}x(x^{2} - 3x + 2)^{n}*-sin(\frac{1}{12}pix^{2})*\frac{1}{12}pi*2x}{12} + \frac{p^{3}i^{3}*3x^{2}(x^{2} - 3x + 2)^{n}sin(\frac{1}{12}pix^{2})}{216} + \frac{p^{3}i^{3}x^{3}((x^{2} - 3x + 2)^{n}((0)ln(x^{2} - 3x + 2) + \frac{(n)(2x - 3 + 0)}{(x^{2} - 3x + 2)}))sin(\frac{1}{12}pix^{2})}{216} + \frac{p^{3}i^{3}x^{3}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})*\frac{1}{12}pi*2x}{216}\\=&\frac{-96nx^{4}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{4}} + \frac{576nx^{3}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{4}} + \frac{96nx^{2}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{3}} + \frac{176n^{2}x^{4}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{4}} - \frac{1056n^{2}x^{3}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{4}} - \frac{32npix^{4}(x^{2} - 3x + 2)^{n}sin(\frac{1}{12}pix^{2})}{3(x^{2} - 3x + 2)^{3}} - \frac{1296nx^{2}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{4}} - \frac{288nx(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{3}} + \frac{2376n^{2}x^{2}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{4}} + \frac{48npix^{3}(x^{2} - 3x + 2)^{n}sin(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{3}} - \frac{12n(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{2}} - \frac{144n^{2}x^{2}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{3}} + \frac{432n^{2}x(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{3}} + \frac{12npix^{2}(x^{2} - 3x + 2)^{n}sin(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{2}} - \frac{96n^{3}x^{4}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{4}} + \frac{576n^{3}x^{3}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{4}} + \frac{16n^{2}pix^{4}(x^{2} - 3x + 2)^{n}sin(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{3}} - \frac{1296n^{3}x^{2}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{4}} - \frac{72n^{2}pix^{3}(x^{2} - 3x + 2)^{n}sin(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{3}} + \frac{2np^{2}i^{2}x^{4}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{3(x^{2} - 3x + 2)^{2}} + \frac{1296nx(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{4}} + \frac{216n(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{3}} - \frac{2376n^{2}x(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{4}} - \frac{72npix^{2}(x^{2} - 3x + 2)^{n}sin(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{3}} - \frac{324n^{2}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{3}} - \frac{24npix(x^{2} - 3x + 2)^{n}sin(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{2}} + \frac{1296n^{3}x(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{4}} + \frac{108n^{2}pix^{2}(x^{2} - 3x + 2)^{n}sin(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{3}} - \frac{2np^{2}i^{2}x^{3}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{2}} + \frac{12n^{2}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{2}} + \frac{48n^{3}x^{2}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{3}} - \frac{144n^{3}x(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{3}} - \frac{12n^{2}pix^{2}(x^{2} - 3x + 2)^{n}sin(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{2}} + \frac{108n^{3}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{3}} + \frac{24n^{2}pix(x^{2} - 3x + 2)^{n}sin(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{2}} - \frac{2npi(x^{2} - 3x + 2)^{n}sin(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)} - \frac{np^{2}i^{2}x^{2}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)} + \frac{16n^{4}x^{4}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{4}} - \frac{96n^{4}x^{3}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{4}} - \frac{16n^{3}pix^{4}(x^{2} - 3x + 2)^{n}sin(\frac{1}{12}pix^{2})}{3(x^{2} - 3x + 2)^{3}} + \frac{216n^{4}x^{2}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{4}} + \frac{24n^{3}pix^{3}(x^{2} - 3x + 2)^{n}sin(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{3}} - \frac{2n^{2}p^{2}i^{2}x^{4}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{3(x^{2} - 3x + 2)^{2}} - \frac{216n^{4}x(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{4}} - \frac{36n^{3}pix^{2}(x^{2} - 3x + 2)^{n}sin(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{3}} + \frac{2n^{2}p^{2}i^{2}x^{3}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{2}} + \frac{np^{3}i^{3}x^{4}(x^{2} - 3x + 2)^{n}sin(\frac{1}{12}pix^{2})}{27(x^{2} - 3x + 2)} - \frac{486n(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{4}} + \frac{891n^{2}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{4}} + \frac{36npix(x^{2} - 3x + 2)^{n}sin(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{3}} - \frac{486n^{3}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{4}} - \frac{54n^{2}pix(x^{2} - 3x + 2)^{n}sin(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{3}} + \frac{9npi(x^{2} - 3x + 2)^{n}sin(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{2}} + \frac{3np^{2}i^{2}x^{2}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{2(x^{2} - 3x + 2)^{2}} + \frac{81n^{4}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{4}} + \frac{18n^{3}pix(x^{2} - 3x + 2)^{n}sin(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{3}} - \frac{9n^{2}pi(x^{2} - 3x + 2)^{n}sin(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{2}} - \frac{3n^{2}p^{2}i^{2}x^{2}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{2(x^{2} - 3x + 2)^{2}} + \frac{np^{2}i^{2}x(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)} - \frac{np^{3}i^{3}x^{3}(x^{2} - 3x + 2)^{n}sin(\frac{1}{12}pix^{2})}{18(x^{2} - 3x + 2)} - \frac{p^{2}i^{2}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{12} + \frac{p^{3}i^{3}x^{2}(x^{2} - 3x + 2)^{n}sin(\frac{1}{12}pix^{2})}{36} + \frac{p^{4}i^{4}x^{4}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{1296}\\ \end{split}\end{equation} \]
注意，变量是区分大小写的。
\[ \begin{equation}\begin{split}【1/1】求函数{({x}^{2} - 3x + 2)}^{n}cos(\frac{pi{x}^{2}}{12}) 关于 x 的 4 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = (x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( (x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})\right)}{dx}\\=&((x^{2} - 3x + 2)^{n}((0)ln(x^{2} - 3x + 2) + \frac{(n)(2x - 3 + 0)}{(x^{2} - 3x + 2)}))cos(\frac{1}{12}pix^{2}) + (x^{2} - 3x + 2)^{n}*-sin(\frac{1}{12}pix^{2})*\frac{1}{12}pi*2x\\=&\frac{2nx(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)} - \frac{3n(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)} - \frac{pix(x^{2} - 3x + 2)^{n}sin(\frac{1}{12}pix^{2})}{6}\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( \frac{2nx(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)} - \frac{3n(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)} - \frac{pix(x^{2} - 3x + 2)^{n}sin(\frac{1}{12}pix^{2})}{6}\right)}{dx}\\=&2(\frac{-(2x - 3 + 0)}{(x^{2} - 3x + 2)^{2}})nx(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2}) + \frac{2n(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)} + \frac{2nx((x^{2} - 3x + 2)^{n}((0)ln(x^{2} - 3x + 2) + \frac{(n)(2x - 3 + 0)}{(x^{2} - 3x + 2)}))cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)} + \frac{2nx(x^{2} - 3x + 2)^{n}*-sin(\frac{1}{12}pix^{2})*\frac{1}{12}pi*2x}{(x^{2} - 3x + 2)} - 3(\frac{-(2x - 3 + 0)}{(x^{2} - 3x + 2)^{2}})n(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2}) - \frac{3n((x^{2} - 3x + 2)^{n}((0)ln(x^{2} - 3x + 2) + \frac{(n)(2x - 3 + 0)}{(x^{2} - 3x + 2)}))cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)} - \frac{3n(x^{2} - 3x + 2)^{n}*-sin(\frac{1}{12}pix^{2})*\frac{1}{12}pi*2x}{(x^{2} - 3x + 2)} - \frac{pi(x^{2} - 3x + 2)^{n}sin(\frac{1}{12}pix^{2})}{6} - \frac{pix((x^{2} - 3x + 2)^{n}((0)ln(x^{2} - 3x + 2) + \frac{(n)(2x - 3 + 0)}{(x^{2} - 3x + 2)}))sin(\frac{1}{12}pix^{2})}{6} - \frac{pix(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})*\frac{1}{12}pi*2x}{6}\\=&\frac{-4nx^{2}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{2}} + \frac{12nx(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{2}} + \frac{2n(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)} + \frac{4n^{2}x^{2}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{2}} - \frac{12n^{2}x(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{2}} - \frac{2npix^{2}(x^{2} - 3x + 2)^{n}sin(\frac{1}{12}pix^{2})}{3(x^{2} - 3x + 2)} - \frac{9n(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{2}} + \frac{9n^{2}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{2}} + \frac{npix(x^{2} - 3x + 2)^{n}sin(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)} - \frac{pi(x^{2} - 3x + 2)^{n}sin(\frac{1}{12}pix^{2})}{6} - \frac{p^{2}i^{2}x^{2}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{36}\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( \frac{-4nx^{2}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{2}} + \frac{12nx(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{2}} + \frac{2n(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)} + \frac{4n^{2}x^{2}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{2}} - \frac{12n^{2}x(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{2}} - \frac{2npix^{2}(x^{2} - 3x + 2)^{n}sin(\frac{1}{12}pix^{2})}{3(x^{2} - 3x + 2)} - \frac{9n(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{2}} + \frac{9n^{2}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{2}} + \frac{npix(x^{2} - 3x + 2)^{n}sin(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)} - \frac{pi(x^{2} - 3x + 2)^{n}sin(\frac{1}{12}pix^{2})}{6} - \frac{p^{2}i^{2}x^{2}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{36}\right)}{dx}\\=&-4(\frac{-2(2x - 3 + 0)}{(x^{2} - 3x + 2)^{3}})nx^{2}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2}) - \frac{4n*2x(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{2}} - \frac{4nx^{2}((x^{2} - 3x + 2)^{n}((0)ln(x^{2} - 3x + 2) + \frac{(n)(2x - 3 + 0)}{(x^{2} - 3x + 2)}))cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{2}} - \frac{4nx^{2}(x^{2} - 3x + 2)^{n}*-sin(\frac{1}{12}pix^{2})*\frac{1}{12}pi*2x}{(x^{2} - 3x + 2)^{2}} + 12(\frac{-2(2x - 3 + 0)}{(x^{2} - 3x + 2)^{3}})nx(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2}) + \frac{12n(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{2}} + \frac{12nx((x^{2} - 3x + 2)^{n}((0)ln(x^{2} - 3x + 2) + \frac{(n)(2x - 3 + 0)}{(x^{2} - 3x + 2)}))cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{2}} + \frac{12nx(x^{2} - 3x + 2)^{n}*-sin(\frac{1}{12}pix^{2})*\frac{1}{12}pi*2x}{(x^{2} - 3x + 2)^{2}} + 2(\frac{-(2x - 3 + 0)}{(x^{2} - 3x + 2)^{2}})n(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2}) + \frac{2n((x^{2} - 3x + 2)^{n}((0)ln(x^{2} - 3x + 2) + \frac{(n)(2x - 3 + 0)}{(x^{2} - 3x + 2)}))cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)} + \frac{2n(x^{2} - 3x + 2)^{n}*-sin(\frac{1}{12}pix^{2})*\frac{1}{12}pi*2x}{(x^{2} - 3x + 2)} + 4(\frac{-2(2x - 3 + 0)}{(x^{2} - 3x + 2)^{3}})n^{2}x^{2}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2}) + \frac{4n^{2}*2x(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{2}} + \frac{4n^{2}x^{2}((x^{2} - 3x + 2)^{n}((0)ln(x^{2} - 3x + 2) + \frac{(n)(2x - 3 + 0)}{(x^{2} - 3x + 2)}))cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{2}} + \frac{4n^{2}x^{2}(x^{2} - 3x + 2)^{n}*-sin(\frac{1}{12}pix^{2})*\frac{1}{12}pi*2x}{(x^{2} - 3x + 2)^{2}} - 12(\frac{-2(2x - 3 + 0)}{(x^{2} - 3x + 2)^{3}})n^{2}x(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2}) - \frac{12n^{2}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{2}} - \frac{12n^{2}x((x^{2} - 3x + 2)^{n}((0)ln(x^{2} - 3x + 2) + \frac{(n)(2x - 3 + 0)}{(x^{2} - 3x + 2)}))cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{2}} - \frac{12n^{2}x(x^{2} - 3x + 2)^{n}*-sin(\frac{1}{12}pix^{2})*\frac{1}{12}pi*2x}{(x^{2} - 3x + 2)^{2}} - \frac{2(\frac{-(2x - 3 + 0)}{(x^{2} - 3x + 2)^{2}})npix^{2}(x^{2} - 3x + 2)^{n}sin(\frac{1}{12}pix^{2})}{3} - \frac{2npi*2x(x^{2} - 3x + 2)^{n}sin(\frac{1}{12}pix^{2})}{3(x^{2} - 3x + 2)} - \frac{2npix^{2}((x^{2} - 3x + 2)^{n}((0)ln(x^{2} - 3x + 2) + \frac{(n)(2x - 3 + 0)}{(x^{2} - 3x + 2)}))sin(\frac{1}{12}pix^{2})}{3(x^{2} - 3x + 2)} - \frac{2npix^{2}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})*\frac{1}{12}pi*2x}{3(x^{2} - 3x + 2)} - 9(\frac{-2(2x - 3 + 0)}{(x^{2} - 3x + 2)^{3}})n(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2}) - \frac{9n((x^{2} - 3x + 2)^{n}((0)ln(x^{2} - 3x + 2) + \frac{(n)(2x - 3 + 0)}{(x^{2} - 3x + 2)}))cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{2}} - \frac{9n(x^{2} - 3x + 2)^{n}*-sin(\frac{1}{12}pix^{2})*\frac{1}{12}pi*2x}{(x^{2} - 3x + 2)^{2}} + 9(\frac{-2(2x - 3 + 0)}{(x^{2} - 3x + 2)^{3}})n^{2}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2}) + \frac{9n^{2}((x^{2} - 3x + 2)^{n}((0)ln(x^{2} - 3x + 2) + \frac{(n)(2x - 3 + 0)}{(x^{2} - 3x + 2)}))cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{2}} + \frac{9n^{2}(x^{2} - 3x + 2)^{n}*-sin(\frac{1}{12}pix^{2})*\frac{1}{12}pi*2x}{(x^{2} - 3x + 2)^{2}} + (\frac{-(2x - 3 + 0)}{(x^{2} - 3x + 2)^{2}})npix(x^{2} - 3x + 2)^{n}sin(\frac{1}{12}pix^{2}) + \frac{npi(x^{2} - 3x + 2)^{n}sin(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)} + \frac{npix((x^{2} - 3x + 2)^{n}((0)ln(x^{2} - 3x + 2) + \frac{(n)(2x - 3 + 0)}{(x^{2} - 3x + 2)}))sin(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)} + \frac{npix(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})*\frac{1}{12}pi*2x}{(x^{2} - 3x + 2)} - \frac{pi((x^{2} - 3x + 2)^{n}((0)ln(x^{2} - 3x + 2) + \frac{(n)(2x - 3 + 0)}{(x^{2} - 3x + 2)}))sin(\frac{1}{12}pix^{2})}{6} - \frac{pi(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})*\frac{1}{12}pi*2x}{6} - \frac{p^{2}i^{2}*2x(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{36} - \frac{p^{2}i^{2}x^{2}((x^{2} - 3x + 2)^{n}((0)ln(x^{2} - 3x + 2) + \frac{(n)(2x - 3 + 0)}{(x^{2} - 3x + 2)}))cos(\frac{1}{12}pix^{2})}{36} - \frac{p^{2}i^{2}x^{2}(x^{2} - 3x + 2)^{n}*-sin(\frac{1}{12}pix^{2})*\frac{1}{12}pi*2x}{36}\\=&\frac{16nx^{3}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{3}} - \frac{72nx^{2}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{3}} - \frac{12nx(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{2}} - \frac{24n^{2}x^{3}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{3}} + \frac{108n^{2}x^{2}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{3}} + \frac{2npix^{3}(x^{2} - 3x + 2)^{n}sin(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{2}} + \frac{108nx(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{3}} + \frac{18n(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{2}} - \frac{162n^{2}x(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{3}} - \frac{6npix^{2}(x^{2} - 3x + 2)^{n}sin(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{2}} + \frac{12n^{2}x(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{2}} - \frac{18n^{2}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{2}} - \frac{2npix(x^{2} - 3x + 2)^{n}sin(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)} + \frac{8n^{3}x^{3}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{3}} - \frac{36n^{3}x^{2}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{3}} - \frac{2n^{2}pix^{3}(x^{2} - 3x + 2)^{n}sin(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{2}} + \frac{54n^{3}x(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{3}} + \frac{6n^{2}pix^{2}(x^{2} - 3x + 2)^{n}sin(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{2}} - \frac{np^{2}i^{2}x^{3}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{6(x^{2} - 3x + 2)} - \frac{54n(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{3}} + \frac{81n^{2}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{3}} + \frac{9npix(x^{2} - 3x + 2)^{n}sin(\frac{1}{12}pix^{2})}{2(x^{2} - 3x + 2)^{2}} - \frac{27n^{3}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{3}} - \frac{9n^{2}pix(x^{2} - 3x + 2)^{n}sin(\frac{1}{12}pix^{2})}{2(x^{2} - 3x + 2)^{2}} + \frac{3npi(x^{2} - 3x + 2)^{n}sin(\frac{1}{12}pix^{2})}{2(x^{2} - 3x + 2)} + \frac{np^{2}i^{2}x^{2}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{4(x^{2} - 3x + 2)} - \frac{p^{2}i^{2}x(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{12} + \frac{p^{3}i^{3}x^{3}(x^{2} - 3x + 2)^{n}sin(\frac{1}{12}pix^{2})}{216}\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( \frac{16nx^{3}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{3}} - \frac{72nx^{2}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{3}} - \frac{12nx(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{2}} - \frac{24n^{2}x^{3}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{3}} + \frac{108n^{2}x^{2}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{3}} + \frac{2npix^{3}(x^{2} - 3x + 2)^{n}sin(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{2}} + \frac{108nx(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{3}} + \frac{18n(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{2}} - \frac{162n^{2}x(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{3}} - \frac{6npix^{2}(x^{2} - 3x + 2)^{n}sin(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{2}} + \frac{12n^{2}x(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{2}} - \frac{18n^{2}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{2}} - \frac{2npix(x^{2} - 3x + 2)^{n}sin(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)} + \frac{8n^{3}x^{3}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{3}} - \frac{36n^{3}x^{2}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{3}} - \frac{2n^{2}pix^{3}(x^{2} - 3x + 2)^{n}sin(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{2}} + \frac{54n^{3}x(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{3}} + \frac{6n^{2}pix^{2}(x^{2} - 3x + 2)^{n}sin(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{2}} - \frac{np^{2}i^{2}x^{3}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{6(x^{2} - 3x + 2)} - \frac{54n(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{3}} + \frac{81n^{2}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{3}} + \frac{9npix(x^{2} - 3x + 2)^{n}sin(\frac{1}{12}pix^{2})}{2(x^{2} - 3x + 2)^{2}} - \frac{27n^{3}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{3}} - \frac{9n^{2}pix(x^{2} - 3x + 2)^{n}sin(\frac{1}{12}pix^{2})}{2(x^{2} - 3x + 2)^{2}} + \frac{3npi(x^{2} - 3x + 2)^{n}sin(\frac{1}{12}pix^{2})}{2(x^{2} - 3x + 2)} + \frac{np^{2}i^{2}x^{2}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{4(x^{2} - 3x + 2)} - \frac{p^{2}i^{2}x(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{12} + \frac{p^{3}i^{3}x^{3}(x^{2} - 3x + 2)^{n}sin(\frac{1}{12}pix^{2})}{216}\right)}{dx}\\=&16(\frac{-3(2x - 3 + 0)}{(x^{2} - 3x + 2)^{4}})nx^{3}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2}) + \frac{16n*3x^{2}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{3}} + \frac{16nx^{3}((x^{2} - 3x + 2)^{n}((0)ln(x^{2} - 3x + 2) + \frac{(n)(2x - 3 + 0)}{(x^{2} - 3x + 2)}))cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{3}} + \frac{16nx^{3}(x^{2} - 3x + 2)^{n}*-sin(\frac{1}{12}pix^{2})*\frac{1}{12}pi*2x}{(x^{2} - 3x + 2)^{3}} - 72(\frac{-3(2x - 3 + 0)}{(x^{2} - 3x + 2)^{4}})nx^{2}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2}) - \frac{72n*2x(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{3}} - \frac{72nx^{2}((x^{2} - 3x + 2)^{n}((0)ln(x^{2} - 3x + 2) + \frac{(n)(2x - 3 + 0)}{(x^{2} - 3x + 2)}))cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{3}} - \frac{72nx^{2}(x^{2} - 3x + 2)^{n}*-sin(\frac{1}{12}pix^{2})*\frac{1}{12}pi*2x}{(x^{2} - 3x + 2)^{3}} - 12(\frac{-2(2x - 3 + 0)}{(x^{2} - 3x + 2)^{3}})nx(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2}) - \frac{12n(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{2}} - \frac{12nx((x^{2} - 3x + 2)^{n}((0)ln(x^{2} - 3x + 2) + \frac{(n)(2x - 3 + 0)}{(x^{2} - 3x + 2)}))cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{2}} - \frac{12nx(x^{2} - 3x + 2)^{n}*-sin(\frac{1}{12}pix^{2})*\frac{1}{12}pi*2x}{(x^{2} - 3x + 2)^{2}} - 24(\frac{-3(2x - 3 + 0)}{(x^{2} - 3x + 2)^{4}})n^{2}x^{3}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2}) - \frac{24n^{2}*3x^{2}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{3}} - \frac{24n^{2}x^{3}((x^{2} - 3x + 2)^{n}((0)ln(x^{2} - 3x + 2) + \frac{(n)(2x - 3 + 0)}{(x^{2} - 3x + 2)}))cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{3}} - \frac{24n^{2}x^{3}(x^{2} - 3x + 2)^{n}*-sin(\frac{1}{12}pix^{2})*\frac{1}{12}pi*2x}{(x^{2} - 3x + 2)^{3}} + 108(\frac{-3(2x - 3 + 0)}{(x^{2} - 3x + 2)^{4}})n^{2}x^{2}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2}) + \frac{108n^{2}*2x(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{3}} + \frac{108n^{2}x^{2}((x^{2} - 3x + 2)^{n}((0)ln(x^{2} - 3x + 2) + \frac{(n)(2x - 3 + 0)}{(x^{2} - 3x + 2)}))cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{3}} + \frac{108n^{2}x^{2}(x^{2} - 3x + 2)^{n}*-sin(\frac{1}{12}pix^{2})*\frac{1}{12}pi*2x}{(x^{2} - 3x + 2)^{3}} + 2(\frac{-2(2x - 3 + 0)}{(x^{2} - 3x + 2)^{3}})npix^{3}(x^{2} - 3x + 2)^{n}sin(\frac{1}{12}pix^{2}) + \frac{2npi*3x^{2}(x^{2} - 3x + 2)^{n}sin(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{2}} + \frac{2npix^{3}((x^{2} - 3x + 2)^{n}((0)ln(x^{2} - 3x + 2) + \frac{(n)(2x - 3 + 0)}{(x^{2} - 3x + 2)}))sin(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{2}} + \frac{2npix^{3}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})*\frac{1}{12}pi*2x}{(x^{2} - 3x + 2)^{2}} + 108(\frac{-3(2x - 3 + 0)}{(x^{2} - 3x + 2)^{4}})nx(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2}) + \frac{108n(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{3}} + \frac{108nx((x^{2} - 3x + 2)^{n}((0)ln(x^{2} - 3x + 2) + \frac{(n)(2x - 3 + 0)}{(x^{2} - 3x + 2)}))cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{3}} + \frac{108nx(x^{2} - 3x + 2)^{n}*-sin(\frac{1}{12}pix^{2})*\frac{1}{12}pi*2x}{(x^{2} - 3x + 2)^{3}} + 18(\frac{-2(2x - 3 + 0)}{(x^{2} - 3x + 2)^{3}})n(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2}) + \frac{18n((x^{2} - 3x + 2)^{n}((0)ln(x^{2} - 3x + 2) + \frac{(n)(2x - 3 + 0)}{(x^{2} - 3x + 2)}))cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{2}} + \frac{18n(x^{2} - 3x + 2)^{n}*-sin(\frac{1}{12}pix^{2})*\frac{1}{12}pi*2x}{(x^{2} - 3x + 2)^{2}} - 162(\frac{-3(2x - 3 + 0)}{(x^{2} - 3x + 2)^{4}})n^{2}x(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2}) - \frac{162n^{2}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{3}} - \frac{162n^{2}x((x^{2} - 3x + 2)^{n}((0)ln(x^{2} - 3x + 2) + \frac{(n)(2x - 3 + 0)}{(x^{2} - 3x + 2)}))cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{3}} - \frac{162n^{2}x(x^{2} - 3x + 2)^{n}*-sin(\frac{1}{12}pix^{2})*\frac{1}{12}pi*2x}{(x^{2} - 3x + 2)^{3}} - 6(\frac{-2(2x - 3 + 0)}{(x^{2} - 3x + 2)^{3}})npix^{2}(x^{2} - 3x + 2)^{n}sin(\frac{1}{12}pix^{2}) - \frac{6npi*2x(x^{2} - 3x + 2)^{n}sin(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{2}} - \frac{6npix^{2}((x^{2} - 3x + 2)^{n}((0)ln(x^{2} - 3x + 2) + \frac{(n)(2x - 3 + 0)}{(x^{2} - 3x + 2)}))sin(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{2}} - \frac{6npix^{2}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})*\frac{1}{12}pi*2x}{(x^{2} - 3x + 2)^{2}} + 12(\frac{-2(2x - 3 + 0)}{(x^{2} - 3x + 2)^{3}})n^{2}x(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2}) + \frac{12n^{2}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{2}} + \frac{12n^{2}x((x^{2} - 3x + 2)^{n}((0)ln(x^{2} - 3x + 2) + \frac{(n)(2x - 3 + 0)}{(x^{2} - 3x + 2)}))cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{2}} + \frac{12n^{2}x(x^{2} - 3x + 2)^{n}*-sin(\frac{1}{12}pix^{2})*\frac{1}{12}pi*2x}{(x^{2} - 3x + 2)^{2}} - 18(\frac{-2(2x - 3 + 0)}{(x^{2} - 3x + 2)^{3}})n^{2}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2}) - \frac{18n^{2}((x^{2} - 3x + 2)^{n}((0)ln(x^{2} - 3x + 2) + \frac{(n)(2x - 3 + 0)}{(x^{2} - 3x + 2)}))cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{2}} - \frac{18n^{2}(x^{2} - 3x + 2)^{n}*-sin(\frac{1}{12}pix^{2})*\frac{1}{12}pi*2x}{(x^{2} - 3x + 2)^{2}} - 2(\frac{-(2x - 3 + 0)}{(x^{2} - 3x + 2)^{2}})npix(x^{2} - 3x + 2)^{n}sin(\frac{1}{12}pix^{2}) - \frac{2npi(x^{2} - 3x + 2)^{n}sin(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)} - \frac{2npix((x^{2} - 3x + 2)^{n}((0)ln(x^{2} - 3x + 2) + \frac{(n)(2x - 3 + 0)}{(x^{2} - 3x + 2)}))sin(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)} - \frac{2npix(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})*\frac{1}{12}pi*2x}{(x^{2} - 3x + 2)} + 8(\frac{-3(2x - 3 + 0)}{(x^{2} - 3x + 2)^{4}})n^{3}x^{3}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2}) + \frac{8n^{3}*3x^{2}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{3}} + \frac{8n^{3}x^{3}((x^{2} - 3x + 2)^{n}((0)ln(x^{2} - 3x + 2) + \frac{(n)(2x - 3 + 0)}{(x^{2} - 3x + 2)}))cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{3}} + \frac{8n^{3}x^{3}(x^{2} - 3x + 2)^{n}*-sin(\frac{1}{12}pix^{2})*\frac{1}{12}pi*2x}{(x^{2} - 3x + 2)^{3}} - 36(\frac{-3(2x - 3 + 0)}{(x^{2} - 3x + 2)^{4}})n^{3}x^{2}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2}) - \frac{36n^{3}*2x(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{3}} - \frac{36n^{3}x^{2}((x^{2} - 3x + 2)^{n}((0)ln(x^{2} - 3x + 2) + \frac{(n)(2x - 3 + 0)}{(x^{2} - 3x + 2)}))cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{3}} - \frac{36n^{3}x^{2}(x^{2} - 3x + 2)^{n}*-sin(\frac{1}{12}pix^{2})*\frac{1}{12}pi*2x}{(x^{2} - 3x + 2)^{3}} - 2(\frac{-2(2x - 3 + 0)}{(x^{2} - 3x + 2)^{3}})n^{2}pix^{3}(x^{2} - 3x + 2)^{n}sin(\frac{1}{12}pix^{2}) - \frac{2n^{2}pi*3x^{2}(x^{2} - 3x + 2)^{n}sin(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{2}} - \frac{2n^{2}pix^{3}((x^{2} - 3x + 2)^{n}((0)ln(x^{2} - 3x + 2) + \frac{(n)(2x - 3 + 0)}{(x^{2} - 3x + 2)}))sin(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{2}} - \frac{2n^{2}pix^{3}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})*\frac{1}{12}pi*2x}{(x^{2} - 3x + 2)^{2}} + 54(\frac{-3(2x - 3 + 0)}{(x^{2} - 3x + 2)^{4}})n^{3}x(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2}) + \frac{54n^{3}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{3}} + \frac{54n^{3}x((x^{2} - 3x + 2)^{n}((0)ln(x^{2} - 3x + 2) + \frac{(n)(2x - 3 + 0)}{(x^{2} - 3x + 2)}))cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{3}} + \frac{54n^{3}x(x^{2} - 3x + 2)^{n}*-sin(\frac{1}{12}pix^{2})*\frac{1}{12}pi*2x}{(x^{2} - 3x + 2)^{3}} + 6(\frac{-2(2x - 3 + 0)}{(x^{2} - 3x + 2)^{3}})n^{2}pix^{2}(x^{2} - 3x + 2)^{n}sin(\frac{1}{12}pix^{2}) + \frac{6n^{2}pi*2x(x^{2} - 3x + 2)^{n}sin(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{2}} + \frac{6n^{2}pix^{2}((x^{2} - 3x + 2)^{n}((0)ln(x^{2} - 3x + 2) + \frac{(n)(2x - 3 + 0)}{(x^{2} - 3x + 2)}))sin(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{2}} + \frac{6n^{2}pix^{2}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})*\frac{1}{12}pi*2x}{(x^{2} - 3x + 2)^{2}} - \frac{(\frac{-(2x - 3 + 0)}{(x^{2} - 3x + 2)^{2}})np^{2}i^{2}x^{3}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{6} - \frac{np^{2}i^{2}*3x^{2}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{6(x^{2} - 3x + 2)} - \frac{np^{2}i^{2}x^{3}((x^{2} - 3x + 2)^{n}((0)ln(x^{2} - 3x + 2) + \frac{(n)(2x - 3 + 0)}{(x^{2} - 3x + 2)}))cos(\frac{1}{12}pix^{2})}{6(x^{2} - 3x + 2)} - \frac{np^{2}i^{2}x^{3}(x^{2} - 3x + 2)^{n}*-sin(\frac{1}{12}pix^{2})*\frac{1}{12}pi*2x}{6(x^{2} - 3x + 2)} - 54(\frac{-3(2x - 3 + 0)}{(x^{2} - 3x + 2)^{4}})n(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2}) - \frac{54n((x^{2} - 3x + 2)^{n}((0)ln(x^{2} - 3x + 2) + \frac{(n)(2x - 3 + 0)}{(x^{2} - 3x + 2)}))cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{3}} - \frac{54n(x^{2} - 3x + 2)^{n}*-sin(\frac{1}{12}pix^{2})*\frac{1}{12}pi*2x}{(x^{2} - 3x + 2)^{3}} + 81(\frac{-3(2x - 3 + 0)}{(x^{2} - 3x + 2)^{4}})n^{2}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2}) + \frac{81n^{2}((x^{2} - 3x + 2)^{n}((0)ln(x^{2} - 3x + 2) + \frac{(n)(2x - 3 + 0)}{(x^{2} - 3x + 2)}))cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{3}} + \frac{81n^{2}(x^{2} - 3x + 2)^{n}*-sin(\frac{1}{12}pix^{2})*\frac{1}{12}pi*2x}{(x^{2} - 3x + 2)^{3}} + \frac{9(\frac{-2(2x - 3 + 0)}{(x^{2} - 3x + 2)^{3}})npix(x^{2} - 3x + 2)^{n}sin(\frac{1}{12}pix^{2})}{2} + \frac{9npi(x^{2} - 3x + 2)^{n}sin(\frac{1}{12}pix^{2})}{2(x^{2} - 3x + 2)^{2}} + \frac{9npix((x^{2} - 3x + 2)^{n}((0)ln(x^{2} - 3x + 2) + \frac{(n)(2x - 3 + 0)}{(x^{2} - 3x + 2)}))sin(\frac{1}{12}pix^{2})}{2(x^{2} - 3x + 2)^{2}} + \frac{9npix(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})*\frac{1}{12}pi*2x}{2(x^{2} - 3x + 2)^{2}} - 27(\frac{-3(2x - 3 + 0)}{(x^{2} - 3x + 2)^{4}})n^{3}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2}) - \frac{27n^{3}((x^{2} - 3x + 2)^{n}((0)ln(x^{2} - 3x + 2) + \frac{(n)(2x - 3 + 0)}{(x^{2} - 3x + 2)}))cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{3}} - \frac{27n^{3}(x^{2} - 3x + 2)^{n}*-sin(\frac{1}{12}pix^{2})*\frac{1}{12}pi*2x}{(x^{2} - 3x + 2)^{3}} - \frac{9(\frac{-2(2x - 3 + 0)}{(x^{2} - 3x + 2)^{3}})n^{2}pix(x^{2} - 3x + 2)^{n}sin(\frac{1}{12}pix^{2})}{2} - \frac{9n^{2}pi(x^{2} - 3x + 2)^{n}sin(\frac{1}{12}pix^{2})}{2(x^{2} - 3x + 2)^{2}} - \frac{9n^{2}pix((x^{2} - 3x + 2)^{n}((0)ln(x^{2} - 3x + 2) + \frac{(n)(2x - 3 + 0)}{(x^{2} - 3x + 2)}))sin(\frac{1}{12}pix^{2})}{2(x^{2} - 3x + 2)^{2}} - \frac{9n^{2}pix(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})*\frac{1}{12}pi*2x}{2(x^{2} - 3x + 2)^{2}} + \frac{3(\frac{-(2x - 3 + 0)}{(x^{2} - 3x + 2)^{2}})npi(x^{2} - 3x + 2)^{n}sin(\frac{1}{12}pix^{2})}{2} + \frac{3npi((x^{2} - 3x + 2)^{n}((0)ln(x^{2} - 3x + 2) + \frac{(n)(2x - 3 + 0)}{(x^{2} - 3x + 2)}))sin(\frac{1}{12}pix^{2})}{2(x^{2} - 3x + 2)} + \frac{3npi(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})*\frac{1}{12}pi*2x}{2(x^{2} - 3x + 2)} + \frac{(\frac{-(2x - 3 + 0)}{(x^{2} - 3x + 2)^{2}})np^{2}i^{2}x^{2}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{4} + \frac{np^{2}i^{2}*2x(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{4(x^{2} - 3x + 2)} + \frac{np^{2}i^{2}x^{2}((x^{2} - 3x + 2)^{n}((0)ln(x^{2} - 3x + 2) + \frac{(n)(2x - 3 + 0)}{(x^{2} - 3x + 2)}))cos(\frac{1}{12}pix^{2})}{4(x^{2} - 3x + 2)} + \frac{np^{2}i^{2}x^{2}(x^{2} - 3x + 2)^{n}*-sin(\frac{1}{12}pix^{2})*\frac{1}{12}pi*2x}{4(x^{2} - 3x + 2)} - \frac{p^{2}i^{2}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{12} - \frac{p^{2}i^{2}x((x^{2} - 3x + 2)^{n}((0)ln(x^{2} - 3x + 2) + \frac{(n)(2x - 3 + 0)}{(x^{2} - 3x + 2)}))cos(\frac{1}{12}pix^{2})}{12} - \frac{p^{2}i^{2}x(x^{2} - 3x + 2)^{n}*-sin(\frac{1}{12}pix^{2})*\frac{1}{12}pi*2x}{12} + \frac{p^{3}i^{3}*3x^{2}(x^{2} - 3x + 2)^{n}sin(\frac{1}{12}pix^{2})}{216} + \frac{p^{3}i^{3}x^{3}((x^{2} - 3x + 2)^{n}((0)ln(x^{2} - 3x + 2) + \frac{(n)(2x - 3 + 0)}{(x^{2} - 3x + 2)}))sin(\frac{1}{12}pix^{2})}{216} + \frac{p^{3}i^{3}x^{3}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})*\frac{1}{12}pi*2x}{216}\\=&\frac{-96nx^{4}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{4}} + \frac{576nx^{3}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{4}} + \frac{96nx^{2}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{3}} + \frac{176n^{2}x^{4}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{4}} - \frac{1056n^{2}x^{3}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{4}} - \frac{32npix^{4}(x^{2} - 3x + 2)^{n}sin(\frac{1}{12}pix^{2})}{3(x^{2} - 3x + 2)^{3}} - \frac{1296nx^{2}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{4}} - \frac{288nx(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{3}} + \frac{2376n^{2}x^{2}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{4}} + \frac{48npix^{3}(x^{2} - 3x + 2)^{n}sin(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{3}} - \frac{12n(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{2}} - \frac{144n^{2}x^{2}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{3}} + \frac{432n^{2}x(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{3}} + \frac{12npix^{2}(x^{2} - 3x + 2)^{n}sin(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{2}} - \frac{96n^{3}x^{4}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{4}} + \frac{576n^{3}x^{3}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{4}} + \frac{16n^{2}pix^{4}(x^{2} - 3x + 2)^{n}sin(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{3}} - \frac{1296n^{3}x^{2}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{4}} - \frac{72n^{2}pix^{3}(x^{2} - 3x + 2)^{n}sin(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{3}} + \frac{2np^{2}i^{2}x^{4}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{3(x^{2} - 3x + 2)^{2}} + \frac{1296nx(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{4}} + \frac{216n(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{3}} - \frac{2376n^{2}x(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{4}} - \frac{72npix^{2}(x^{2} - 3x + 2)^{n}sin(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{3}} - \frac{324n^{2}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{3}} - \frac{24npix(x^{2} - 3x + 2)^{n}sin(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{2}} + \frac{1296n^{3}x(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{4}} + \frac{108n^{2}pix^{2}(x^{2} - 3x + 2)^{n}sin(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{3}} - \frac{2np^{2}i^{2}x^{3}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{2}} + \frac{12n^{2}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{2}} + \frac{48n^{3}x^{2}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{3}} - \frac{144n^{3}x(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{3}} - \frac{12n^{2}pix^{2}(x^{2} - 3x + 2)^{n}sin(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{2}} + \frac{108n^{3}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{3}} + \frac{24n^{2}pix(x^{2} - 3x + 2)^{n}sin(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{2}} - \frac{2npi(x^{2} - 3x + 2)^{n}sin(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)} - \frac{np^{2}i^{2}x^{2}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)} + \frac{16n^{4}x^{4}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{4}} - \frac{96n^{4}x^{3}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{4}} - \frac{16n^{3}pix^{4}(x^{2} - 3x + 2)^{n}sin(\frac{1}{12}pix^{2})}{3(x^{2} - 3x + 2)^{3}} + \frac{216n^{4}x^{2}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{4}} + \frac{24n^{3}pix^{3}(x^{2} - 3x + 2)^{n}sin(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{3}} - \frac{2n^{2}p^{2}i^{2}x^{4}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{3(x^{2} - 3x + 2)^{2}} - \frac{216n^{4}x(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{4}} - \frac{36n^{3}pix^{2}(x^{2} - 3x + 2)^{n}sin(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{3}} + \frac{2n^{2}p^{2}i^{2}x^{3}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{2}} + \frac{np^{3}i^{3}x^{4}(x^{2} - 3x + 2)^{n}sin(\frac{1}{12}pix^{2})}{27(x^{2} - 3x + 2)} - \frac{486n(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{4}} + \frac{891n^{2}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{4}} + \frac{36npix(x^{2} - 3x + 2)^{n}sin(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{3}} - \frac{486n^{3}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{4}} - \frac{54n^{2}pix(x^{2} - 3x + 2)^{n}sin(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{3}} + \frac{9npi(x^{2} - 3x + 2)^{n}sin(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{2}} + \frac{3np^{2}i^{2}x^{2}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{2(x^{2} - 3x + 2)^{2}} + \frac{81n^{4}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{4}} + \frac{18n^{3}pix(x^{2} - 3x + 2)^{n}sin(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{3}} - \frac{9n^{2}pi(x^{2} - 3x + 2)^{n}sin(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)^{2}} - \frac{3n^{2}p^{2}i^{2}x^{2}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{2(x^{2} - 3x + 2)^{2}} + \frac{np^{2}i^{2}x(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{(x^{2} - 3x + 2)} - \frac{np^{3}i^{3}x^{3}(x^{2} - 3x + 2)^{n}sin(\frac{1}{12}pix^{2})}{18(x^{2} - 3x + 2)} - \frac{p^{2}i^{2}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{12} + \frac{p^{3}i^{3}x^{2}(x^{2} - 3x + 2)^{n}sin(\frac{1}{12}pix^{2})}{36} + \frac{p^{4}i^{4}x^{4}(x^{2} - 3x + 2)^{n}cos(\frac{1}{12}pix^{2})}{1296}\\ \end{split}\end{equation} \]
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