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。
\[ \begin{equation}\begin{split}【1/1】求函数sin(sin(sin(sin(x)))) 关于 x 的 4 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( sin(sin(sin(sin(x))))\right)}{dx}\\=&cos(sin(sin(sin(x))))cos(sin(sin(x)))cos(sin(x))cos(x)\\=&cos(sin(x))cos(sin(sin(x)))cos(x)cos(sin(sin(sin(x))))\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( cos(sin(x))cos(sin(sin(x)))cos(x)cos(sin(sin(sin(x))))\right)}{dx}\\=&-sin(sin(x))cos(x)cos(sin(sin(x)))cos(x)cos(sin(sin(sin(x)))) + cos(sin(x))*-sin(sin(sin(x)))cos(sin(x))cos(x)cos(x)cos(sin(sin(sin(x)))) + cos(sin(x))cos(sin(sin(x)))*-sin(x)cos(sin(sin(sin(x)))) + cos(sin(x))cos(sin(sin(x)))cos(x)*-sin(sin(sin(sin(x))))cos(sin(sin(x)))cos(sin(x))cos(x)\\=&-sin(sin(x))cos^{2}(x)cos(sin(sin(x)))cos(sin(sin(sin(x)))) - sin(sin(sin(x)))cos^{2}(sin(x))cos^{2}(x)cos(sin(sin(sin(x)))) - sin(x)cos(sin(sin(x)))cos(sin(x))cos(sin(sin(sin(x)))) - sin(sin(sin(sin(x))))cos^{2}(sin(sin(x)))cos^{2}(sin(x))cos^{2}(x)\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( -sin(sin(x))cos^{2}(x)cos(sin(sin(x)))cos(sin(sin(sin(x)))) - sin(sin(sin(x)))cos^{2}(sin(x))cos^{2}(x)cos(sin(sin(sin(x)))) - sin(x)cos(sin(sin(x)))cos(sin(x))cos(sin(sin(sin(x)))) - sin(sin(sin(sin(x))))cos^{2}(sin(sin(x)))cos^{2}(sin(x))cos^{2}(x)\right)}{dx}\\=&-cos(sin(x))cos(x)cos^{2}(x)cos(sin(sin(x)))cos(sin(sin(sin(x)))) - sin(sin(x))*-2cos(x)sin(x)cos(sin(sin(x)))cos(sin(sin(sin(x)))) - sin(sin(x))cos^{2}(x)*-sin(sin(sin(x)))cos(sin(x))cos(x)cos(sin(sin(sin(x)))) - sin(sin(x))cos^{2}(x)cos(sin(sin(x)))*-sin(sin(sin(sin(x))))cos(sin(sin(x)))cos(sin(x))cos(x) - cos(sin(sin(x)))cos(sin(x))cos(x)cos^{2}(sin(x))cos^{2}(x)cos(sin(sin(sin(x)))) - sin(sin(sin(x)))*-2cos(sin(x))sin(sin(x))cos(x)cos^{2}(x)cos(sin(sin(sin(x)))) - sin(sin(sin(x)))cos^{2}(sin(x))*-2cos(x)sin(x)cos(sin(sin(sin(x)))) - sin(sin(sin(x)))cos^{2}(sin(x))cos^{2}(x)*-sin(sin(sin(sin(x))))cos(sin(sin(x)))cos(sin(x))cos(x) - cos(x)cos(sin(sin(x)))cos(sin(x))cos(sin(sin(sin(x)))) - sin(x)*-sin(sin(sin(x)))cos(sin(x))cos(x)cos(sin(x))cos(sin(sin(sin(x)))) - sin(x)cos(sin(sin(x)))*-sin(sin(x))cos(x)cos(sin(sin(sin(x)))) - sin(x)cos(sin(sin(x)))cos(sin(x))*-sin(sin(sin(sin(x))))cos(sin(sin(x)))cos(sin(x))cos(x) - cos(sin(sin(sin(x))))cos(sin(sin(x)))cos(sin(x))cos(x)cos^{2}(sin(sin(x)))cos^{2}(sin(x))cos^{2}(x) - sin(sin(sin(sin(x))))*-2cos(sin(sin(x)))sin(sin(sin(x)))cos(sin(x))cos(x)cos^{2}(sin(x))cos^{2}(x) - sin(sin(sin(sin(x))))cos^{2}(sin(sin(x)))*-2cos(sin(x))sin(sin(x))cos(x)cos^{2}(x) - sin(sin(sin(sin(x))))cos^{2}(sin(sin(x)))cos^{2}(sin(x))*-2cos(x)sin(x)\\=&-cos^{3}(x)cos(sin(x))cos(sin(sin(x)))cos(sin(sin(sin(x)))) + 3sin(x)sin(sin(x))cos(x)cos(sin(sin(x)))cos(sin(sin(sin(x)))) + 2sin(sin(sin(x)))sin(sin(sin(sin(x))))cos(sin(sin(x)))cos^{3}(x)cos^{3}(sin(x)) + sin(sin(x))sin(sin(sin(sin(x))))cos^{2}(sin(sin(x)))cos(sin(x))cos^{3}(x) - cos(sin(sin(x)))cos^{3}(x)cos^{3}(sin(x))cos(sin(sin(sin(x)))) + 3sin(sin(sin(x)))sin(sin(x))cos^{3}(x)cos(sin(x))cos(sin(sin(sin(x)))) + 2sin(x)sin(sin(sin(x)))cos^{2}(sin(x))cos(x)cos(sin(sin(sin(x)))) + sin(sin(sin(x)))sin(sin(sin(sin(x))))cos^{3}(x)cos^{3}(sin(x))cos(sin(sin(x))) - cos(x)cos(sin(sin(x)))cos(sin(x))cos(sin(sin(sin(x)))) + sin(sin(sin(x)))sin(x)cos(x)cos^{2}(sin(x))cos(sin(sin(sin(x)))) + 2sin(sin(sin(sin(x))))sin(sin(x))cos(sin(x))cos^{3}(x)cos^{2}(sin(sin(x))) + sin(x)sin(sin(sin(sin(x))))cos^{2}(sin(x))cos^{2}(sin(sin(x)))cos(x) - cos^{3}(sin(x))cos^{3}(sin(sin(x)))cos^{3}(x)cos(sin(sin(sin(x)))) + 2sin(x)sin(sin(sin(sin(x))))cos(x)cos^{2}(sin(x))cos^{2}(sin(sin(x)))\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( -cos^{3}(x)cos(sin(x))cos(sin(sin(x)))cos(sin(sin(sin(x)))) + 3sin(x)sin(sin(x))cos(x)cos(sin(sin(x)))cos(sin(sin(sin(x)))) + 2sin(sin(sin(x)))sin(sin(sin(sin(x))))cos(sin(sin(x)))cos^{3}(x)cos^{3}(sin(x)) + sin(sin(x))sin(sin(sin(sin(x))))cos^{2}(sin(sin(x)))cos(sin(x))cos^{3}(x) - cos(sin(sin(x)))cos^{3}(x)cos^{3}(sin(x))cos(sin(sin(sin(x)))) + 3sin(sin(sin(x)))sin(sin(x))cos^{3}(x)cos(sin(x))cos(sin(sin(sin(x)))) + 2sin(x)sin(sin(sin(x)))cos^{2}(sin(x))cos(x)cos(sin(sin(sin(x)))) + sin(sin(sin(x)))sin(sin(sin(sin(x))))cos^{3}(x)cos^{3}(sin(x))cos(sin(sin(x))) - cos(x)cos(sin(sin(x)))cos(sin(x))cos(sin(sin(sin(x)))) + sin(sin(sin(x)))sin(x)cos(x)cos^{2}(sin(x))cos(sin(sin(sin(x)))) + 2sin(sin(sin(sin(x))))sin(sin(x))cos(sin(x))cos^{3}(x)cos^{2}(sin(sin(x))) + sin(x)sin(sin(sin(sin(x))))cos^{2}(sin(x))cos^{2}(sin(sin(x)))cos(x) - cos^{3}(sin(x))cos^{3}(sin(sin(x)))cos^{3}(x)cos(sin(sin(sin(x)))) + 2sin(x)sin(sin(sin(sin(x))))cos(x)cos^{2}(sin(x))cos^{2}(sin(sin(x)))\right)}{dx}\\=&--3cos^{2}(x)sin(x)cos(sin(x))cos(sin(sin(x)))cos(sin(sin(sin(x)))) - cos^{3}(x)*-sin(sin(x))cos(x)cos(sin(sin(x)))cos(sin(sin(sin(x)))) - cos^{3}(x)cos(sin(x))*-sin(sin(sin(x)))cos(sin(x))cos(x)cos(sin(sin(sin(x)))) - cos^{3}(x)cos(sin(x))cos(sin(sin(x)))*-sin(sin(sin(sin(x))))cos(sin(sin(x)))cos(sin(x))cos(x) + 3cos(x)sin(sin(x))cos(x)cos(sin(sin(x)))cos(sin(sin(sin(x)))) + 3sin(x)cos(sin(x))cos(x)cos(x)cos(sin(sin(x)))cos(sin(sin(sin(x)))) + 3sin(x)sin(sin(x))*-sin(x)cos(sin(sin(x)))cos(sin(sin(sin(x)))) + 3sin(x)sin(sin(x))cos(x)*-sin(sin(sin(x)))cos(sin(x))cos(x)cos(sin(sin(sin(x)))) + 3sin(x)sin(sin(x))cos(x)cos(sin(sin(x)))*-sin(sin(sin(sin(x))))cos(sin(sin(x)))cos(sin(x))cos(x) + 2cos(sin(sin(x)))cos(sin(x))cos(x)sin(sin(sin(sin(x))))cos(sin(sin(x)))cos^{3}(x)cos^{3}(sin(x)) + 2sin(sin(sin(x)))cos(sin(sin(sin(x))))cos(sin(sin(x)))cos(sin(x))cos(x)cos(sin(sin(x)))cos^{3}(x)cos^{3}(sin(x)) + 2sin(sin(sin(x)))sin(sin(sin(sin(x))))*-sin(sin(sin(x)))cos(sin(x))cos(x)cos^{3}(x)cos^{3}(sin(x)) + 2sin(sin(sin(x)))sin(sin(sin(sin(x))))cos(sin(sin(x)))*-3cos^{2}(x)sin(x)cos^{3}(sin(x)) + 2sin(sin(sin(x)))sin(sin(sin(sin(x))))cos(sin(sin(x)))cos^{3}(x)*-3cos^{2}(sin(x))sin(sin(x))cos(x) + cos(sin(x))cos(x)sin(sin(sin(sin(x))))cos^{2}(sin(sin(x)))cos(sin(x))cos^{3}(x) + sin(sin(x))cos(sin(sin(sin(x))))cos(sin(sin(x)))cos(sin(x))cos(x)cos^{2}(sin(sin(x)))cos(sin(x))cos^{3}(x) + sin(sin(x))sin(sin(sin(sin(x))))*-2cos(sin(sin(x)))sin(sin(sin(x)))cos(sin(x))cos(x)cos(sin(x))cos^{3}(x) + sin(sin(x))sin(sin(sin(sin(x))))cos^{2}(sin(sin(x)))*-sin(sin(x))cos(x)cos^{3}(x) + sin(sin(x))sin(sin(sin(sin(x))))cos^{2}(sin(sin(x)))cos(sin(x))*-3cos^{2}(x)sin(x) - -sin(sin(sin(x)))cos(sin(x))cos(x)cos^{3}(x)cos^{3}(sin(x))cos(sin(sin(sin(x)))) - cos(sin(sin(x)))*-3cos^{2}(x)sin(x)cos^{3}(sin(x))cos(sin(sin(sin(x)))) - cos(sin(sin(x)))cos^{3}(x)*-3cos^{2}(sin(x))sin(sin(x))cos(x)cos(sin(sin(sin(x)))) - cos(sin(sin(x)))cos^{3}(x)cos^{3}(sin(x))*-sin(sin(sin(sin(x))))cos(sin(sin(x)))cos(sin(x))cos(x) + 3cos(sin(sin(x)))cos(sin(x))cos(x)sin(sin(x))cos^{3}(x)cos(sin(x))cos(sin(sin(sin(x)))) + 3sin(sin(sin(x)))cos(sin(x))cos(x)cos^{3}(x)cos(sin(x))cos(sin(sin(sin(x)))) + 3sin(sin(sin(x)))sin(sin(x))*-3cos^{2}(x)sin(x)cos(sin(x))cos(sin(sin(sin(x)))) + 3sin(sin(sin(x)))sin(sin(x))cos^{3}(x)*-sin(sin(x))cos(x)cos(sin(sin(sin(x)))) + 3sin(sin(sin(x)))sin(sin(x))cos^{3}(x)cos(sin(x))*-sin(sin(sin(sin(x))))cos(sin(sin(x)))cos(sin(x))cos(x) + 2cos(x)sin(sin(sin(x)))cos^{2}(sin(x))cos(x)cos(sin(sin(sin(x)))) + 2sin(x)cos(sin(sin(x)))cos(sin(x))cos(x)cos^{2}(sin(x))cos(x)cos(sin(sin(sin(x)))) + 2sin(x)sin(sin(sin(x)))*-2cos(sin(x))sin(sin(x))cos(x)cos(x)cos(sin(sin(sin(x)))) + 2sin(x)sin(sin(sin(x)))cos^{2}(sin(x))*-sin(x)cos(sin(sin(sin(x)))) + 2sin(x)sin(sin(sin(x)))cos^{2}(sin(x))cos(x)*-sin(sin(sin(sin(x))))cos(sin(sin(x)))cos(sin(x))cos(x) + cos(sin(sin(x)))cos(sin(x))cos(x)sin(sin(sin(sin(x))))cos^{3}(x)cos^{3}(sin(x))cos(sin(sin(x))) + sin(sin(sin(x)))cos(sin(sin(sin(x))))cos(sin(sin(x)))cos(sin(x))cos(x)cos^{3}(x)cos^{3}(sin(x))cos(sin(sin(x))) + sin(sin(sin(x)))sin(sin(sin(sin(x))))*-3cos^{2}(x)sin(x)cos^{3}(sin(x))cos(sin(sin(x))) + sin(sin(sin(x)))sin(sin(sin(sin(x))))cos^{3}(x)*-3cos^{2}(sin(x))sin(sin(x))cos(x)cos(sin(sin(x))) + sin(sin(sin(x)))sin(sin(sin(sin(x))))cos^{3}(x)cos^{3}(sin(x))*-sin(sin(sin(x)))cos(sin(x))cos(x) - -sin(x)cos(sin(sin(x)))cos(sin(x))cos(sin(sin(sin(x)))) - cos(x)*-sin(sin(sin(x)))cos(sin(x))cos(x)cos(sin(x))cos(sin(sin(sin(x)))) - cos(x)cos(sin(sin(x)))*-sin(sin(x))cos(x)cos(sin(sin(sin(x)))) - cos(x)cos(sin(sin(x)))cos(sin(x))*-sin(sin(sin(sin(x))))cos(sin(sin(x)))cos(sin(x))cos(x) + cos(sin(sin(x)))cos(sin(x))cos(x)sin(x)cos(x)cos^{2}(sin(x))cos(sin(sin(sin(x)))) + sin(sin(sin(x)))cos(x)cos(x)cos^{2}(sin(x))cos(sin(sin(sin(x)))) + sin(sin(sin(x)))sin(x)*-sin(x)cos^{2}(sin(x))cos(sin(sin(sin(x)))) + sin(sin(sin(x)))sin(x)cos(x)*-2cos(sin(x))sin(sin(x))cos(x)cos(sin(sin(sin(x)))) + sin(sin(sin(x)))sin(x)cos(x)cos^{2}(sin(x))*-sin(sin(sin(sin(x))))cos(sin(sin(x)))cos(sin(x))cos(x) + 2cos(sin(sin(sin(x))))cos(sin(sin(x)))cos(sin(x))cos(x)sin(sin(x))cos(sin(x))cos^{3}(x)cos^{2}(sin(sin(x))) + 2sin(sin(sin(sin(x))))cos(sin(x))cos(x)cos(sin(x))cos^{3}(x)cos^{2}(sin(sin(x))) + 2sin(sin(sin(sin(x))))sin(sin(x))*-sin(sin(x))cos(x)cos^{3}(x)cos^{2}(sin(sin(x))) + 2sin(sin(sin(sin(x))))sin(sin(x))cos(sin(x))*-3cos^{2}(x)sin(x)cos^{2}(sin(sin(x))) + 2sin(sin(sin(sin(x))))sin(sin(x))cos(sin(x))cos^{3}(x)*-2cos(sin(sin(x)))sin(sin(sin(x)))cos(sin(x))cos(x) + cos(x)sin(sin(sin(sin(x))))cos^{2}(sin(x))cos^{2}(sin(sin(x)))cos(x) + sin(x)cos(sin(sin(sin(x))))cos(sin(sin(x)))cos(sin(x))cos(x)cos^{2}(sin(x))cos^{2}(sin(sin(x)))cos(x) + sin(x)sin(sin(sin(sin(x))))*-2cos(sin(x))sin(sin(x))cos(x)cos^{2}(sin(sin(x)))cos(x) + sin(x)sin(sin(sin(sin(x))))cos^{2}(sin(x))*-2cos(sin(sin(x)))sin(sin(sin(x)))cos(sin(x))cos(x)cos(x) + sin(x)sin(sin(sin(sin(x))))cos^{2}(sin(x))cos^{2}(sin(sin(x)))*-sin(x) - -3cos^{2}(sin(x))sin(sin(x))cos(x)cos^{3}(sin(sin(x)))cos^{3}(x)cos(sin(sin(sin(x)))) - cos^{3}(sin(x))*-3cos^{2}(sin(sin(x)))sin(sin(sin(x)))cos(sin(x))cos(x)cos^{3}(x)cos(sin(sin(sin(x)))) - cos^{3}(sin(x))cos^{3}(sin(sin(x)))*-3cos^{2}(x)sin(x)cos(sin(sin(sin(x)))) - cos^{3}(sin(x))cos^{3}(sin(sin(x)))cos^{3}(x)*-sin(sin(sin(sin(x))))cos(sin(sin(x)))cos(sin(x))cos(x) + 2cos(x)sin(sin(sin(sin(x))))cos(x)cos^{2}(sin(x))cos^{2}(sin(sin(x))) + 2sin(x)cos(sin(sin(sin(x))))cos(sin(sin(x)))cos(sin(x))cos(x)cos(x)cos^{2}(sin(x))cos^{2}(sin(sin(x))) + 2sin(x)sin(sin(sin(sin(x))))*-sin(x)cos^{2}(sin(x))cos^{2}(sin(sin(x))) + 2sin(x)sin(sin(sin(sin(x))))cos(x)*-2cos(sin(x))sin(sin(x))cos(x)cos^{2}(sin(sin(x))) + 2sin(x)sin(sin(sin(sin(x))))cos(x)cos^{2}(sin(x))*-2cos(sin(sin(x)))sin(sin(sin(x)))cos(sin(x))cos(x)\\=&6sin(x)cos^{2}(x)cos(sin(x))cos(sin(sin(x)))cos(sin(sin(sin(x)))) + 3sin(sin(sin(x)))cos^{4}(sin(x))cos^{2}(sin(sin(x)))cos^{4}(x)cos(sin(sin(sin(x)))) + 3sin(sin(x))cos^{4}(x)cos^{2}(sin(x))cos(sin(sin(x)))cos(sin(sin(sin(x)))) + sin(sin(x))cos^{2}(sin(x))cos^{3}(sin(sin(x)))cos^{4}(x)cos(sin(sin(sin(x)))) + 2sin(sin(x))cos^{3}(sin(sin(x)))cos^{4}(x)cos(sin(sin(sin(x))))cos^{2}(sin(x)) + 5sin(x)cos(sin(sin(x)))cos^{2}(x)cos^{3}(sin(x))cos(sin(sin(sin(x)))) - 6sin(sin(sin(x)))sin(x)sin(sin(sin(sin(x))))cos(sin(sin(x)))cos^{2}(x)cos^{3}(sin(x)) - 2sin(sin(sin(sin(x))))sin(sin(x))sin(sin(sin(x)))cos(sin(sin(x)))cos^{4}(x)cos^{2}(sin(x)) - 3sin(x)sin(sin(sin(sin(x))))sin(sin(x))cos^{2}(sin(sin(x)))cos(sin(x))cos^{2}(x) + sin(x)cos^{2}(x)cos^{3}(sin(x))cos(sin(sin(x)))cos(sin(sin(sin(x)))) + 3sin(sin(x))cos^{4}(x)cos(sin(sin(x)))cos^{2}(sin(x))cos(sin(sin(sin(x)))) - 4sin(sin(x))sin(sin(sin(sin(x))))sin(sin(sin(x)))cos^{2}(sin(x))cos(sin(sin(x)))cos^{4}(x) - 3sin(sin(x))sin(x)sin(sin(sin(sin(x))))cos^{2}(x)cos(sin(x))cos^{2}(sin(sin(x))) - 6sin(sin(x))sin(sin(sin(sin(x))))sin(sin(sin(x)))cos^{4}(x)cos(sin(sin(x)))cos^{2}(sin(x)) + 3sin(x)cos^{3}(sin(x))cos^{3}(sin(sin(x)))cos^{2}(x)cos(sin(sin(sin(x)))) - 2sin(sin(sin(sin(x))))sin(x)sin(sin(sin(x)))cos^{3}(sin(x))cos^{2}(x)cos(sin(sin(x))) - 4sin(sin(x))sin(sin(sin(x)))sin(x)cos^{2}(x)cos(sin(x))cos(sin(sin(sin(x)))) - 9sin(sin(sin(x)))sin(x)sin(sin(x))cos^{2}(x)cos(sin(x))cos(sin(sin(sin(x)))) + 3sin(sin(x))cos^{4}(x)cos^{2}(sin(x))cos^{3}(sin(sin(x)))cos(sin(sin(sin(x)))) + 3sin(sin(sin(x)))cos^{4}(sin(x))cos^{4}(x)cos^{2}(sin(sin(x)))cos(sin(sin(sin(x)))) + 3sin(x)cos^{2}(x)cos^{3}(sin(sin(x)))cos^{3}(sin(x))cos(sin(sin(sin(x)))) + sin(sin(sin(sin(x))))cos^{2}(sin(sin(x)))cos^{4}(sin(x))cos^{4}(x) - 3sin(sin(sin(x)))sin(x)sin(sin(sin(sin(x))))cos^{2}(x)cos^{3}(sin(x))cos(sin(sin(x))) - 3sin(sin(x))sin(sin(sin(sin(x))))sin(sin(sin(x)))cos^{2}(sin(x))cos^{4}(x)cos(sin(sin(x))) - 3sin(sin(sin(x)))sin(sin(sin(sin(x))))sin(sin(x))cos^{2}(sin(x))cos^{4}(x)cos(sin(sin(x))) + 4sin(sin(sin(x)))cos^{2}(x)cos^{2}(sin(x))cos(sin(sin(sin(x)))) + 3sin(sin(sin(sin(x))))cos^{4}(x)cos^{4}(sin(x))cos^{2}(sin(sin(x))) - 2sin(sin(x))sin(x)sin(sin(sin(x)))cos(sin(x))cos^{2}(x)cos(sin(sin(sin(x)))) - 6sin(sin(sin(sin(x))))sin(x)sin(sin(x))cos(sin(x))cos^{2}(x)cos^{2}(sin(sin(x))) - 2sin(x)sin(sin(sin(sin(x))))sin(sin(sin(x)))cos^{2}(x)cos^{3}(sin(x))cos(sin(sin(x))) + sin(sin(sin(sin(x))))cos^{2}(sin(sin(x)))cos^{4}(x)cos^{2}(sin(x)) + 3sin(sin(sin(x)))cos^{4}(x)cos^{2}(sin(x))cos(sin(sin(sin(x)))) - 3sin^{2}(x)sin(sin(x))cos(sin(sin(x)))cos(sin(sin(sin(x)))) - 2sin(sin(x))sin(sin(sin(sin(x))))sin(x)cos^{2}(x)cos(sin(x))cos^{2}(sin(sin(x))) - 4sin(sin(sin(sin(x))))sin(x)sin(sin(sin(x)))cos^{2}(x)cos^{3}(sin(x))cos(sin(sin(x))) + 4sin(sin(x))cos^{2}(x)cos(sin(sin(x)))cos(sin(sin(sin(x)))) + sin(sin(sin(sin(x))))cos^{2}(sin(sin(x)))cos^{2}(x)cos^{2}(sin(x)) + sin(sin(x))cos^{4}(x)cos(sin(sin(x)))cos(sin(sin(sin(x)))) - sin(sin(sin(x)))sin^{2}(x)cos^{2}(sin(x))cos(sin(sin(sin(x)))) - 4sin(sin(x))sin(sin(sin(sin(x))))sin(x)cos(sin(x))cos^{2}(x)cos^{2}(sin(sin(x))) - sin(sin(sin(x)))sin(sin(sin(sin(x))))sin(x)cos^{3}(sin(x))cos^{2}(x)cos(sin(sin(x))) + 2sin(sin(sin(sin(x))))cos^{4}(x)cos^{2}(sin(x))cos^{2}(sin(sin(x))) + sin(sin(sin(sin(x))))cos^{2}(sin(x))cos^{4}(x)cos^{2}(sin(sin(x))) - 3sin^{2}(sin(x))sin(sin(sin(sin(x))))cos^{4}(x)cos^{2}(sin(sin(x))) - 2sin^{2}(x)sin(sin(sin(x)))cos^{2}(sin(x))cos(sin(sin(sin(x)))) - 2sin(sin(sin(sin(x))))sin^{2}(sin(sin(x)))cos^{4}(x)cos^{4}(sin(x)) + 3sin(sin(sin(sin(x))))cos^{2}(x)cos^{2}(sin(x))cos^{2}(sin(sin(x))) + sin(sin(sin(x)))cos^{2}(sin(x))cos^{4}(x)cos(sin(sin(sin(x)))) - 3sin^{2}(sin(x))sin(sin(sin(x)))cos^{4}(x)cos(sin(sin(sin(x)))) - 3sin(sin(x))sin(x)sin(sin(sin(x)))cos^{2}(x)cos(sin(x))cos(sin(sin(sin(x)))) - sin^{2}(x)sin(sin(sin(sin(x))))cos^{2}(sin(sin(x)))cos^{2}(sin(x)) + sin(x)cos(sin(sin(x)))cos(sin(x))cos(sin(sin(sin(x)))) + sin(sin(sin(sin(x))))cos^{4}(sin(sin(x)))cos^{4}(sin(x))cos^{4}(x) + sin(sin(sin(x)))cos^{4}(x)cos^{4}(sin(x))cos(sin(sin(sin(x)))) - 2sin^{2}(x)sin(sin(sin(sin(x))))cos^{2}(sin(x))cos^{2}(sin(sin(x))) - sin(sin(sin(sin(x))))sin^{2}(sin(sin(x)))cos^{4}(sin(x))cos^{4}(x)\\ \end{split}\end{equation} \]
注意，变量是区分大小写的。
\[ \begin{equation}\begin{split}【1/1】求函数sin(sin(sin(sin(x)))) 关于 x 的 4 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( sin(sin(sin(sin(x))))\right)}{dx}\\=&cos(sin(sin(sin(x))))cos(sin(sin(x)))cos(sin(x))cos(x)\\=&cos(sin(x))cos(sin(sin(x)))cos(x)cos(sin(sin(sin(x))))\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( cos(sin(x))cos(sin(sin(x)))cos(x)cos(sin(sin(sin(x))))\right)}{dx}\\=&-sin(sin(x))cos(x)cos(sin(sin(x)))cos(x)cos(sin(sin(sin(x)))) + cos(sin(x))*-sin(sin(sin(x)))cos(sin(x))cos(x)cos(x)cos(sin(sin(sin(x)))) + cos(sin(x))cos(sin(sin(x)))*-sin(x)cos(sin(sin(sin(x)))) + cos(sin(x))cos(sin(sin(x)))cos(x)*-sin(sin(sin(sin(x))))cos(sin(sin(x)))cos(sin(x))cos(x)\\=&-sin(sin(x))cos^{2}(x)cos(sin(sin(x)))cos(sin(sin(sin(x)))) - sin(sin(sin(x)))cos^{2}(sin(x))cos^{2}(x)cos(sin(sin(sin(x)))) - sin(x)cos(sin(sin(x)))cos(sin(x))cos(sin(sin(sin(x)))) - sin(sin(sin(sin(x))))cos^{2}(sin(sin(x)))cos^{2}(sin(x))cos^{2}(x)\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( -sin(sin(x))cos^{2}(x)cos(sin(sin(x)))cos(sin(sin(sin(x)))) - sin(sin(sin(x)))cos^{2}(sin(x))cos^{2}(x)cos(sin(sin(sin(x)))) - sin(x)cos(sin(sin(x)))cos(sin(x))cos(sin(sin(sin(x)))) - sin(sin(sin(sin(x))))cos^{2}(sin(sin(x)))cos^{2}(sin(x))cos^{2}(x)\right)}{dx}\\=&-cos(sin(x))cos(x)cos^{2}(x)cos(sin(sin(x)))cos(sin(sin(sin(x)))) - sin(sin(x))*-2cos(x)sin(x)cos(sin(sin(x)))cos(sin(sin(sin(x)))) - sin(sin(x))cos^{2}(x)*-sin(sin(sin(x)))cos(sin(x))cos(x)cos(sin(sin(sin(x)))) - sin(sin(x))cos^{2}(x)cos(sin(sin(x)))*-sin(sin(sin(sin(x))))cos(sin(sin(x)))cos(sin(x))cos(x) - cos(sin(sin(x)))cos(sin(x))cos(x)cos^{2}(sin(x))cos^{2}(x)cos(sin(sin(sin(x)))) - sin(sin(sin(x)))*-2cos(sin(x))sin(sin(x))cos(x)cos^{2}(x)cos(sin(sin(sin(x)))) - sin(sin(sin(x)))cos^{2}(sin(x))*-2cos(x)sin(x)cos(sin(sin(sin(x)))) - sin(sin(sin(x)))cos^{2}(sin(x))cos^{2}(x)*-sin(sin(sin(sin(x))))cos(sin(sin(x)))cos(sin(x))cos(x) - cos(x)cos(sin(sin(x)))cos(sin(x))cos(sin(sin(sin(x)))) - sin(x)*-sin(sin(sin(x)))cos(sin(x))cos(x)cos(sin(x))cos(sin(sin(sin(x)))) - sin(x)cos(sin(sin(x)))*-sin(sin(x))cos(x)cos(sin(sin(sin(x)))) - sin(x)cos(sin(sin(x)))cos(sin(x))*-sin(sin(sin(sin(x))))cos(sin(sin(x)))cos(sin(x))cos(x) - cos(sin(sin(sin(x))))cos(sin(sin(x)))cos(sin(x))cos(x)cos^{2}(sin(sin(x)))cos^{2}(sin(x))cos^{2}(x) - sin(sin(sin(sin(x))))*-2cos(sin(sin(x)))sin(sin(sin(x)))cos(sin(x))cos(x)cos^{2}(sin(x))cos^{2}(x) - sin(sin(sin(sin(x))))cos^{2}(sin(sin(x)))*-2cos(sin(x))sin(sin(x))cos(x)cos^{2}(x) - sin(sin(sin(sin(x))))cos^{2}(sin(sin(x)))cos^{2}(sin(x))*-2cos(x)sin(x)\\=&-cos^{3}(x)cos(sin(x))cos(sin(sin(x)))cos(sin(sin(sin(x)))) + 3sin(x)sin(sin(x))cos(x)cos(sin(sin(x)))cos(sin(sin(sin(x)))) + 2sin(sin(sin(x)))sin(sin(sin(sin(x))))cos(sin(sin(x)))cos^{3}(x)cos^{3}(sin(x)) + sin(sin(x))sin(sin(sin(sin(x))))cos^{2}(sin(sin(x)))cos(sin(x))cos^{3}(x) - cos(sin(sin(x)))cos^{3}(x)cos^{3}(sin(x))cos(sin(sin(sin(x)))) + 3sin(sin(sin(x)))sin(sin(x))cos^{3}(x)cos(sin(x))cos(sin(sin(sin(x)))) + 2sin(x)sin(sin(sin(x)))cos^{2}(sin(x))cos(x)cos(sin(sin(sin(x)))) + sin(sin(sin(x)))sin(sin(sin(sin(x))))cos^{3}(x)cos^{3}(sin(x))cos(sin(sin(x))) - cos(x)cos(sin(sin(x)))cos(sin(x))cos(sin(sin(sin(x)))) + sin(sin(sin(x)))sin(x)cos(x)cos^{2}(sin(x))cos(sin(sin(sin(x)))) + 2sin(sin(sin(sin(x))))sin(sin(x))cos(sin(x))cos^{3}(x)cos^{2}(sin(sin(x))) + sin(x)sin(sin(sin(sin(x))))cos^{2}(sin(x))cos^{2}(sin(sin(x)))cos(x) - cos^{3}(sin(x))cos^{3}(sin(sin(x)))cos^{3}(x)cos(sin(sin(sin(x)))) + 2sin(x)sin(sin(sin(sin(x))))cos(x)cos^{2}(sin(x))cos^{2}(sin(sin(x)))\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( -cos^{3}(x)cos(sin(x))cos(sin(sin(x)))cos(sin(sin(sin(x)))) + 3sin(x)sin(sin(x))cos(x)cos(sin(sin(x)))cos(sin(sin(sin(x)))) + 2sin(sin(sin(x)))sin(sin(sin(sin(x))))cos(sin(sin(x)))cos^{3}(x)cos^{3}(sin(x)) + sin(sin(x))sin(sin(sin(sin(x))))cos^{2}(sin(sin(x)))cos(sin(x))cos^{3}(x) - cos(sin(sin(x)))cos^{3}(x)cos^{3}(sin(x))cos(sin(sin(sin(x)))) + 3sin(sin(sin(x)))sin(sin(x))cos^{3}(x)cos(sin(x))cos(sin(sin(sin(x)))) + 2sin(x)sin(sin(sin(x)))cos^{2}(sin(x))cos(x)cos(sin(sin(sin(x)))) + sin(sin(sin(x)))sin(sin(sin(sin(x))))cos^{3}(x)cos^{3}(sin(x))cos(sin(sin(x))) - cos(x)cos(sin(sin(x)))cos(sin(x))cos(sin(sin(sin(x)))) + sin(sin(sin(x)))sin(x)cos(x)cos^{2}(sin(x))cos(sin(sin(sin(x)))) + 2sin(sin(sin(sin(x))))sin(sin(x))cos(sin(x))cos^{3}(x)cos^{2}(sin(sin(x))) + sin(x)sin(sin(sin(sin(x))))cos^{2}(sin(x))cos^{2}(sin(sin(x)))cos(x) - cos^{3}(sin(x))cos^{3}(sin(sin(x)))cos^{3}(x)cos(sin(sin(sin(x)))) + 2sin(x)sin(sin(sin(sin(x))))cos(x)cos^{2}(sin(x))cos^{2}(sin(sin(x)))\right)}{dx}\\=&--3cos^{2}(x)sin(x)cos(sin(x))cos(sin(sin(x)))cos(sin(sin(sin(x)))) - cos^{3}(x)*-sin(sin(x))cos(x)cos(sin(sin(x)))cos(sin(sin(sin(x)))) - cos^{3}(x)cos(sin(x))*-sin(sin(sin(x)))cos(sin(x))cos(x)cos(sin(sin(sin(x)))) - cos^{3}(x)cos(sin(x))cos(sin(sin(x)))*-sin(sin(sin(sin(x))))cos(sin(sin(x)))cos(sin(x))cos(x) + 3cos(x)sin(sin(x))cos(x)cos(sin(sin(x)))cos(sin(sin(sin(x)))) + 3sin(x)cos(sin(x))cos(x)cos(x)cos(sin(sin(x)))cos(sin(sin(sin(x)))) + 3sin(x)sin(sin(x))*-sin(x)cos(sin(sin(x)))cos(sin(sin(sin(x)))) + 3sin(x)sin(sin(x))cos(x)*-sin(sin(sin(x)))cos(sin(x))cos(x)cos(sin(sin(sin(x)))) + 3sin(x)sin(sin(x))cos(x)cos(sin(sin(x)))*-sin(sin(sin(sin(x))))cos(sin(sin(x)))cos(sin(x))cos(x) + 2cos(sin(sin(x)))cos(sin(x))cos(x)sin(sin(sin(sin(x))))cos(sin(sin(x)))cos^{3}(x)cos^{3}(sin(x)) + 2sin(sin(sin(x)))cos(sin(sin(sin(x))))cos(sin(sin(x)))cos(sin(x))cos(x)cos(sin(sin(x)))cos^{3}(x)cos^{3}(sin(x)) + 2sin(sin(sin(x)))sin(sin(sin(sin(x))))*-sin(sin(sin(x)))cos(sin(x))cos(x)cos^{3}(x)cos^{3}(sin(x)) + 2sin(sin(sin(x)))sin(sin(sin(sin(x))))cos(sin(sin(x)))*-3cos^{2}(x)sin(x)cos^{3}(sin(x)) + 2sin(sin(sin(x)))sin(sin(sin(sin(x))))cos(sin(sin(x)))cos^{3}(x)*-3cos^{2}(sin(x))sin(sin(x))cos(x) + cos(sin(x))cos(x)sin(sin(sin(sin(x))))cos^{2}(sin(sin(x)))cos(sin(x))cos^{3}(x) + sin(sin(x))cos(sin(sin(sin(x))))cos(sin(sin(x)))cos(sin(x))cos(x)cos^{2}(sin(sin(x)))cos(sin(x))cos^{3}(x) + sin(sin(x))sin(sin(sin(sin(x))))*-2cos(sin(sin(x)))sin(sin(sin(x)))cos(sin(x))cos(x)cos(sin(x))cos^{3}(x) + sin(sin(x))sin(sin(sin(sin(x))))cos^{2}(sin(sin(x)))*-sin(sin(x))cos(x)cos^{3}(x) + sin(sin(x))sin(sin(sin(sin(x))))cos^{2}(sin(sin(x)))cos(sin(x))*-3cos^{2}(x)sin(x) - -sin(sin(sin(x)))cos(sin(x))cos(x)cos^{3}(x)cos^{3}(sin(x))cos(sin(sin(sin(x)))) - cos(sin(sin(x)))*-3cos^{2}(x)sin(x)cos^{3}(sin(x))cos(sin(sin(sin(x)))) - cos(sin(sin(x)))cos^{3}(x)*-3cos^{2}(sin(x))sin(sin(x))cos(x)cos(sin(sin(sin(x)))) - cos(sin(sin(x)))cos^{3}(x)cos^{3}(sin(x))*-sin(sin(sin(sin(x))))cos(sin(sin(x)))cos(sin(x))cos(x) + 3cos(sin(sin(x)))cos(sin(x))cos(x)sin(sin(x))cos^{3}(x)cos(sin(x))cos(sin(sin(sin(x)))) + 3sin(sin(sin(x)))cos(sin(x))cos(x)cos^{3}(x)cos(sin(x))cos(sin(sin(sin(x)))) + 3sin(sin(sin(x)))sin(sin(x))*-3cos^{2}(x)sin(x)cos(sin(x))cos(sin(sin(sin(x)))) + 3sin(sin(sin(x)))sin(sin(x))cos^{3}(x)*-sin(sin(x))cos(x)cos(sin(sin(sin(x)))) + 3sin(sin(sin(x)))sin(sin(x))cos^{3}(x)cos(sin(x))*-sin(sin(sin(sin(x))))cos(sin(sin(x)))cos(sin(x))cos(x) + 2cos(x)sin(sin(sin(x)))cos^{2}(sin(x))cos(x)cos(sin(sin(sin(x)))) + 2sin(x)cos(sin(sin(x)))cos(sin(x))cos(x)cos^{2}(sin(x))cos(x)cos(sin(sin(sin(x)))) + 2sin(x)sin(sin(sin(x)))*-2cos(sin(x))sin(sin(x))cos(x)cos(x)cos(sin(sin(sin(x)))) + 2sin(x)sin(sin(sin(x)))cos^{2}(sin(x))*-sin(x)cos(sin(sin(sin(x)))) + 2sin(x)sin(sin(sin(x)))cos^{2}(sin(x))cos(x)*-sin(sin(sin(sin(x))))cos(sin(sin(x)))cos(sin(x))cos(x) + cos(sin(sin(x)))cos(sin(x))cos(x)sin(sin(sin(sin(x))))cos^{3}(x)cos^{3}(sin(x))cos(sin(sin(x))) + sin(sin(sin(x)))cos(sin(sin(sin(x))))cos(sin(sin(x)))cos(sin(x))cos(x)cos^{3}(x)cos^{3}(sin(x))cos(sin(sin(x))) + sin(sin(sin(x)))sin(sin(sin(sin(x))))*-3cos^{2}(x)sin(x)cos^{3}(sin(x))cos(sin(sin(x))) + sin(sin(sin(x)))sin(sin(sin(sin(x))))cos^{3}(x)*-3cos^{2}(sin(x))sin(sin(x))cos(x)cos(sin(sin(x))) + sin(sin(sin(x)))sin(sin(sin(sin(x))))cos^{3}(x)cos^{3}(sin(x))*-sin(sin(sin(x)))cos(sin(x))cos(x) - -sin(x)cos(sin(sin(x)))cos(sin(x))cos(sin(sin(sin(x)))) - cos(x)*-sin(sin(sin(x)))cos(sin(x))cos(x)cos(sin(x))cos(sin(sin(sin(x)))) - cos(x)cos(sin(sin(x)))*-sin(sin(x))cos(x)cos(sin(sin(sin(x)))) - cos(x)cos(sin(sin(x)))cos(sin(x))*-sin(sin(sin(sin(x))))cos(sin(sin(x)))cos(sin(x))cos(x) + cos(sin(sin(x)))cos(sin(x))cos(x)sin(x)cos(x)cos^{2}(sin(x))cos(sin(sin(sin(x)))) + sin(sin(sin(x)))cos(x)cos(x)cos^{2}(sin(x))cos(sin(sin(sin(x)))) + sin(sin(sin(x)))sin(x)*-sin(x)cos^{2}(sin(x))cos(sin(sin(sin(x)))) + sin(sin(sin(x)))sin(x)cos(x)*-2cos(sin(x))sin(sin(x))cos(x)cos(sin(sin(sin(x)))) + sin(sin(sin(x)))sin(x)cos(x)cos^{2}(sin(x))*-sin(sin(sin(sin(x))))cos(sin(sin(x)))cos(sin(x))cos(x) + 2cos(sin(sin(sin(x))))cos(sin(sin(x)))cos(sin(x))cos(x)sin(sin(x))cos(sin(x))cos^{3}(x)cos^{2}(sin(sin(x))) + 2sin(sin(sin(sin(x))))cos(sin(x))cos(x)cos(sin(x))cos^{3}(x)cos^{2}(sin(sin(x))) + 2sin(sin(sin(sin(x))))sin(sin(x))*-sin(sin(x))cos(x)cos^{3}(x)cos^{2}(sin(sin(x))) + 2sin(sin(sin(sin(x))))sin(sin(x))cos(sin(x))*-3cos^{2}(x)sin(x)cos^{2}(sin(sin(x))) + 2sin(sin(sin(sin(x))))sin(sin(x))cos(sin(x))cos^{3}(x)*-2cos(sin(sin(x)))sin(sin(sin(x)))cos(sin(x))cos(x) + cos(x)sin(sin(sin(sin(x))))cos^{2}(sin(x))cos^{2}(sin(sin(x)))cos(x) + sin(x)cos(sin(sin(sin(x))))cos(sin(sin(x)))cos(sin(x))cos(x)cos^{2}(sin(x))cos^{2}(sin(sin(x)))cos(x) + sin(x)sin(sin(sin(sin(x))))*-2cos(sin(x))sin(sin(x))cos(x)cos^{2}(sin(sin(x)))cos(x) + sin(x)sin(sin(sin(sin(x))))cos^{2}(sin(x))*-2cos(sin(sin(x)))sin(sin(sin(x)))cos(sin(x))cos(x)cos(x) + sin(x)sin(sin(sin(sin(x))))cos^{2}(sin(x))cos^{2}(sin(sin(x)))*-sin(x) - -3cos^{2}(sin(x))sin(sin(x))cos(x)cos^{3}(sin(sin(x)))cos^{3}(x)cos(sin(sin(sin(x)))) - cos^{3}(sin(x))*-3cos^{2}(sin(sin(x)))sin(sin(sin(x)))cos(sin(x))cos(x)cos^{3}(x)cos(sin(sin(sin(x)))) - cos^{3}(sin(x))cos^{3}(sin(sin(x)))*-3cos^{2}(x)sin(x)cos(sin(sin(sin(x)))) - cos^{3}(sin(x))cos^{3}(sin(sin(x)))cos^{3}(x)*-sin(sin(sin(sin(x))))cos(sin(sin(x)))cos(sin(x))cos(x) + 2cos(x)sin(sin(sin(sin(x))))cos(x)cos^{2}(sin(x))cos^{2}(sin(sin(x))) + 2sin(x)cos(sin(sin(sin(x))))cos(sin(sin(x)))cos(sin(x))cos(x)cos(x)cos^{2}(sin(x))cos^{2}(sin(sin(x))) + 2sin(x)sin(sin(sin(sin(x))))*-sin(x)cos^{2}(sin(x))cos^{2}(sin(sin(x))) + 2sin(x)sin(sin(sin(sin(x))))cos(x)*-2cos(sin(x))sin(sin(x))cos(x)cos^{2}(sin(sin(x))) + 2sin(x)sin(sin(sin(sin(x))))cos(x)cos^{2}(sin(x))*-2cos(sin(sin(x)))sin(sin(sin(x)))cos(sin(x))cos(x)\\=&6sin(x)cos^{2}(x)cos(sin(x))cos(sin(sin(x)))cos(sin(sin(sin(x)))) + 3sin(sin(sin(x)))cos^{4}(sin(x))cos^{2}(sin(sin(x)))cos^{4}(x)cos(sin(sin(sin(x)))) + 3sin(sin(x))cos^{4}(x)cos^{2}(sin(x))cos(sin(sin(x)))cos(sin(sin(sin(x)))) + sin(sin(x))cos^{2}(sin(x))cos^{3}(sin(sin(x)))cos^{4}(x)cos(sin(sin(sin(x)))) + 2sin(sin(x))cos^{3}(sin(sin(x)))cos^{4}(x)cos(sin(sin(sin(x))))cos^{2}(sin(x)) + 5sin(x)cos(sin(sin(x)))cos^{2}(x)cos^{3}(sin(x))cos(sin(sin(sin(x)))) - 6sin(sin(sin(x)))sin(x)sin(sin(sin(sin(x))))cos(sin(sin(x)))cos^{2}(x)cos^{3}(sin(x)) - 2sin(sin(sin(sin(x))))sin(sin(x))sin(sin(sin(x)))cos(sin(sin(x)))cos^{4}(x)cos^{2}(sin(x)) - 3sin(x)sin(sin(sin(sin(x))))sin(sin(x))cos^{2}(sin(sin(x)))cos(sin(x))cos^{2}(x) + sin(x)cos^{2}(x)cos^{3}(sin(x))cos(sin(sin(x)))cos(sin(sin(sin(x)))) + 3sin(sin(x))cos^{4}(x)cos(sin(sin(x)))cos^{2}(sin(x))cos(sin(sin(sin(x)))) - 4sin(sin(x))sin(sin(sin(sin(x))))sin(sin(sin(x)))cos^{2}(sin(x))cos(sin(sin(x)))cos^{4}(x) - 3sin(sin(x))sin(x)sin(sin(sin(sin(x))))cos^{2}(x)cos(sin(x))cos^{2}(sin(sin(x))) - 6sin(sin(x))sin(sin(sin(sin(x))))sin(sin(sin(x)))cos^{4}(x)cos(sin(sin(x)))cos^{2}(sin(x)) + 3sin(x)cos^{3}(sin(x))cos^{3}(sin(sin(x)))cos^{2}(x)cos(sin(sin(sin(x)))) - 2sin(sin(sin(sin(x))))sin(x)sin(sin(sin(x)))cos^{3}(sin(x))cos^{2}(x)cos(sin(sin(x))) - 4sin(sin(x))sin(sin(sin(x)))sin(x)cos^{2}(x)cos(sin(x))cos(sin(sin(sin(x)))) - 9sin(sin(sin(x)))sin(x)sin(sin(x))cos^{2}(x)cos(sin(x))cos(sin(sin(sin(x)))) + 3sin(sin(x))cos^{4}(x)cos^{2}(sin(x))cos^{3}(sin(sin(x)))cos(sin(sin(sin(x)))) + 3sin(sin(sin(x)))cos^{4}(sin(x))cos^{4}(x)cos^{2}(sin(sin(x)))cos(sin(sin(sin(x)))) + 3sin(x)cos^{2}(x)cos^{3}(sin(sin(x)))cos^{3}(sin(x))cos(sin(sin(sin(x)))) + sin(sin(sin(sin(x))))cos^{2}(sin(sin(x)))cos^{4}(sin(x))cos^{4}(x) - 3sin(sin(sin(x)))sin(x)sin(sin(sin(sin(x))))cos^{2}(x)cos^{3}(sin(x))cos(sin(sin(x))) - 3sin(sin(x))sin(sin(sin(sin(x))))sin(sin(sin(x)))cos^{2}(sin(x))cos^{4}(x)cos(sin(sin(x))) - 3sin(sin(sin(x)))sin(sin(sin(sin(x))))sin(sin(x))cos^{2}(sin(x))cos^{4}(x)cos(sin(sin(x))) + 4sin(sin(sin(x)))cos^{2}(x)cos^{2}(sin(x))cos(sin(sin(sin(x)))) + 3sin(sin(sin(sin(x))))cos^{4}(x)cos^{4}(sin(x))cos^{2}(sin(sin(x))) - 2sin(sin(x))sin(x)sin(sin(sin(x)))cos(sin(x))cos^{2}(x)cos(sin(sin(sin(x)))) - 6sin(sin(sin(sin(x))))sin(x)sin(sin(x))cos(sin(x))cos^{2}(x)cos^{2}(sin(sin(x))) - 2sin(x)sin(sin(sin(sin(x))))sin(sin(sin(x)))cos^{2}(x)cos^{3}(sin(x))cos(sin(sin(x))) + sin(sin(sin(sin(x))))cos^{2}(sin(sin(x)))cos^{4}(x)cos^{2}(sin(x)) + 3sin(sin(sin(x)))cos^{4}(x)cos^{2}(sin(x))cos(sin(sin(sin(x)))) - 3sin^{2}(x)sin(sin(x))cos(sin(sin(x)))cos(sin(sin(sin(x)))) - 2sin(sin(x))sin(sin(sin(sin(x))))sin(x)cos^{2}(x)cos(sin(x))cos^{2}(sin(sin(x))) - 4sin(sin(sin(sin(x))))sin(x)sin(sin(sin(x)))cos^{2}(x)cos^{3}(sin(x))cos(sin(sin(x))) + 4sin(sin(x))cos^{2}(x)cos(sin(sin(x)))cos(sin(sin(sin(x)))) + sin(sin(sin(sin(x))))cos^{2}(sin(sin(x)))cos^{2}(x)cos^{2}(sin(x)) + sin(sin(x))cos^{4}(x)cos(sin(sin(x)))cos(sin(sin(sin(x)))) - sin(sin(sin(x)))sin^{2}(x)cos^{2}(sin(x))cos(sin(sin(sin(x)))) - 4sin(sin(x))sin(sin(sin(sin(x))))sin(x)cos(sin(x))cos^{2}(x)cos^{2}(sin(sin(x))) - sin(sin(sin(x)))sin(sin(sin(sin(x))))sin(x)cos^{3}(sin(x))cos^{2}(x)cos(sin(sin(x))) + 2sin(sin(sin(sin(x))))cos^{4}(x)cos^{2}(sin(x))cos^{2}(sin(sin(x))) + sin(sin(sin(sin(x))))cos^{2}(sin(x))cos^{4}(x)cos^{2}(sin(sin(x))) - 3sin^{2}(sin(x))sin(sin(sin(sin(x))))cos^{4}(x)cos^{2}(sin(sin(x))) - 2sin^{2}(x)sin(sin(sin(x)))cos^{2}(sin(x))cos(sin(sin(sin(x)))) - 2sin(sin(sin(sin(x))))sin^{2}(sin(sin(x)))cos^{4}(x)cos^{4}(sin(x)) + 3sin(sin(sin(sin(x))))cos^{2}(x)cos^{2}(sin(x))cos^{2}(sin(sin(x))) + sin(sin(sin(x)))cos^{2}(sin(x))cos^{4}(x)cos(sin(sin(sin(x)))) - 3sin^{2}(sin(x))sin(sin(sin(x)))cos^{4}(x)cos(sin(sin(sin(x)))) - 3sin(sin(x))sin(x)sin(sin(sin(x)))cos^{2}(x)cos(sin(x))cos(sin(sin(sin(x)))) - sin^{2}(x)sin(sin(sin(sin(x))))cos^{2}(sin(sin(x)))cos^{2}(sin(x)) + sin(x)cos(sin(sin(x)))cos(sin(x))cos(sin(sin(sin(x)))) + sin(sin(sin(sin(x))))cos^{4}(sin(sin(x)))cos^{4}(sin(x))cos^{4}(x) + sin(sin(sin(x)))cos^{4}(x)cos^{4}(sin(x))cos(sin(sin(sin(x)))) - 2sin^{2}(x)sin(sin(sin(sin(x))))cos^{2}(sin(x))cos^{2}(sin(sin(x))) - sin(sin(sin(sin(x))))sin^{2}(sin(sin(x)))cos^{4}(sin(x))cos^{4}(x)\\ \end{split}\end{equation} \]
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