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。
\[ \begin{equation}\begin{split}【1/1】求函数lg({(sin(x))}^{6} + {(cos(x))}^{6}) 关于 x 的 4 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = lg(sin^{6}(x) + cos^{6}(x))\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( lg(sin^{6}(x) + cos^{6}(x))\right)}{dx}\\=&\frac{(6sin^{5}(x)cos(x) + -6cos^{5}(x)sin(x))}{ln{10}(sin^{6}(x) + cos^{6}(x))}\\=&\frac{6sin^{5}(x)cos(x)}{(sin^{6}(x) + cos^{6}(x))ln{10}} - \frac{6sin(x)cos^{5}(x)}{(sin^{6}(x) + cos^{6}(x))ln{10}}\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( \frac{6sin^{5}(x)cos(x)}{(sin^{6}(x) + cos^{6}(x))ln{10}} - \frac{6sin(x)cos^{5}(x)}{(sin^{6}(x) + cos^{6}(x))ln{10}}\right)}{dx}\\=&\frac{6(\frac{-(6sin^{5}(x)cos(x) + -6cos^{5}(x)sin(x))}{(sin^{6}(x) + cos^{6}(x))^{2}})sin^{5}(x)cos(x)}{ln{10}} + \frac{6*-0sin^{5}(x)cos(x)}{(sin^{6}(x) + cos^{6}(x))ln^{2}{10}} + \frac{6*5sin^{4}(x)cos(x)cos(x)}{(sin^{6}(x) + cos^{6}(x))ln{10}} + \frac{6sin^{5}(x)*-sin(x)}{(sin^{6}(x) + cos^{6}(x))ln{10}} - \frac{6(\frac{-(6sin^{5}(x)cos(x) + -6cos^{5}(x)sin(x))}{(sin^{6}(x) + cos^{6}(x))^{2}})sin(x)cos^{5}(x)}{ln{10}} - \frac{6*-0sin(x)cos^{5}(x)}{(sin^{6}(x) + cos^{6}(x))ln^{2}{10}} - \frac{6cos(x)cos^{5}(x)}{(sin^{6}(x) + cos^{6}(x))ln{10}} - \frac{6sin(x)*-5cos^{4}(x)sin(x)}{(sin^{6}(x) + cos^{6}(x))ln{10}}\\=&\frac{-36sin^{10}(x)cos^{2}(x)}{(sin^{6}(x) + cos^{6}(x))^{2}ln{10}} + \frac{72sin^{6}(x)cos^{6}(x)}{(sin^{6}(x) + cos^{6}(x))^{2}ln{10}} + \frac{30sin^{4}(x)cos^{2}(x)}{(sin^{6}(x) + cos^{6}(x))ln{10}} + \frac{30sin^{2}(x)cos^{4}(x)}{(sin^{6}(x) + cos^{6}(x))ln{10}} - \frac{36sin^{2}(x)cos^{10}(x)}{(sin^{6}(x) + cos^{6}(x))^{2}ln{10}} - \frac{6cos^{6}(x)}{(sin^{6}(x) + cos^{6}(x))ln{10}} - \frac{6sin^{6}(x)}{(sin^{6}(x) + cos^{6}(x))ln{10}}\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( \frac{-36sin^{10}(x)cos^{2}(x)}{(sin^{6}(x) + cos^{6}(x))^{2}ln{10}} + \frac{72sin^{6}(x)cos^{6}(x)}{(sin^{6}(x) + cos^{6}(x))^{2}ln{10}} + \frac{30sin^{4}(x)cos^{2}(x)}{(sin^{6}(x) + cos^{6}(x))ln{10}} + \frac{30sin^{2}(x)cos^{4}(x)}{(sin^{6}(x) + cos^{6}(x))ln{10}} - \frac{36sin^{2}(x)cos^{10}(x)}{(sin^{6}(x) + cos^{6}(x))^{2}ln{10}} - \frac{6cos^{6}(x)}{(sin^{6}(x) + cos^{6}(x))ln{10}} - \frac{6sin^{6}(x)}{(sin^{6}(x) + cos^{6}(x))ln{10}}\right)}{dx}\\=&\frac{-36(\frac{-2(6sin^{5}(x)cos(x) + -6cos^{5}(x)sin(x))}{(sin^{6}(x) + cos^{6}(x))^{3}})sin^{10}(x)cos^{2}(x)}{ln{10}} - \frac{36*-0sin^{10}(x)cos^{2}(x)}{(sin^{6}(x) + cos^{6}(x))^{2}ln^{2}{10}} - \frac{36*10sin^{9}(x)cos(x)cos^{2}(x)}{(sin^{6}(x) + cos^{6}(x))^{2}ln{10}} - \frac{36sin^{10}(x)*-2cos(x)sin(x)}{(sin^{6}(x) + cos^{6}(x))^{2}ln{10}} + \frac{72(\frac{-2(6sin^{5}(x)cos(x) + -6cos^{5}(x)sin(x))}{(sin^{6}(x) + cos^{6}(x))^{3}})sin^{6}(x)cos^{6}(x)}{ln{10}} + \frac{72*-0sin^{6}(x)cos^{6}(x)}{(sin^{6}(x) + cos^{6}(x))^{2}ln^{2}{10}} + \frac{72*6sin^{5}(x)cos(x)cos^{6}(x)}{(sin^{6}(x) + cos^{6}(x))^{2}ln{10}} + \frac{72sin^{6}(x)*-6cos^{5}(x)sin(x)}{(sin^{6}(x) + cos^{6}(x))^{2}ln{10}} + \frac{30(\frac{-(6sin^{5}(x)cos(x) + -6cos^{5}(x)sin(x))}{(sin^{6}(x) + cos^{6}(x))^{2}})sin^{4}(x)cos^{2}(x)}{ln{10}} + \frac{30*-0sin^{4}(x)cos^{2}(x)}{(sin^{6}(x) + cos^{6}(x))ln^{2}{10}} + \frac{30*4sin^{3}(x)cos(x)cos^{2}(x)}{(sin^{6}(x) + cos^{6}(x))ln{10}} + \frac{30sin^{4}(x)*-2cos(x)sin(x)}{(sin^{6}(x) + cos^{6}(x))ln{10}} + \frac{30(\frac{-(6sin^{5}(x)cos(x) + -6cos^{5}(x)sin(x))}{(sin^{6}(x) + cos^{6}(x))^{2}})sin^{2}(x)cos^{4}(x)}{ln{10}} + \frac{30*-0sin^{2}(x)cos^{4}(x)}{(sin^{6}(x) + cos^{6}(x))ln^{2}{10}} + \frac{30*2sin(x)cos(x)cos^{4}(x)}{(sin^{6}(x) + cos^{6}(x))ln{10}} + \frac{30sin^{2}(x)*-4cos^{3}(x)sin(x)}{(sin^{6}(x) + cos^{6}(x))ln{10}} - \frac{36(\frac{-2(6sin^{5}(x)cos(x) + -6cos^{5}(x)sin(x))}{(sin^{6}(x) + cos^{6}(x))^{3}})sin^{2}(x)cos^{10}(x)}{ln{10}} - \frac{36*-0sin^{2}(x)cos^{10}(x)}{(sin^{6}(x) + cos^{6}(x))^{2}ln^{2}{10}} - \frac{36*2sin(x)cos(x)cos^{10}(x)}{(sin^{6}(x) + cos^{6}(x))^{2}ln{10}} - \frac{36sin^{2}(x)*-10cos^{9}(x)sin(x)}{(sin^{6}(x) + cos^{6}(x))^{2}ln{10}} - \frac{6(\frac{-(6sin^{5}(x)cos(x) + -6cos^{5}(x)sin(x))}{(sin^{6}(x) + cos^{6}(x))^{2}})cos^{6}(x)}{ln{10}} - \frac{6*-0cos^{6}(x)}{(sin^{6}(x) + cos^{6}(x))ln^{2}{10}} - \frac{6*-6cos^{5}(x)sin(x)}{(sin^{6}(x) + cos^{6}(x))ln{10}} - \frac{6(\frac{-(6sin^{5}(x)cos(x) + -6cos^{5}(x)sin(x))}{(sin^{6}(x) + cos^{6}(x))^{2}})sin^{6}(x)}{ln{10}} - \frac{6*-0sin^{6}(x)}{(sin^{6}(x) + cos^{6}(x))ln^{2}{10}} - \frac{6*6sin^{5}(x)cos(x)}{(sin^{6}(x) + cos^{6}(x))ln{10}}\\=&\frac{432sin^{15}(x)cos^{3}(x)}{(sin^{6}(x) + cos^{6}(x))^{3}ln{10}} - \frac{1296sin^{11}(x)cos^{7}(x)}{(sin^{6}(x) + cos^{6}(x))^{3}ln{10}} - \frac{540sin^{9}(x)cos^{3}(x)}{(sin^{6}(x) + cos^{6}(x))^{2}ln{10}} + \frac{108sin^{11}(x)cos(x)}{(sin^{6}(x) + cos^{6}(x))^{2}ln{10}} + \frac{1296sin^{7}(x)cos^{11}(x)}{(sin^{6}(x) + cos^{6}(x))^{3}ln{10}} + \frac{648sin^{5}(x)cos^{7}(x)}{(sin^{6}(x) + cos^{6}(x))^{2}ln{10}} - \frac{648sin^{7}(x)cos^{5}(x)}{(sin^{6}(x) + cos^{6}(x))^{2}ln{10}} + \frac{96sin(x)cos^{5}(x)}{(sin^{6}(x) + cos^{6}(x))ln{10}} - \frac{108sin(x)cos^{11}(x)}{(sin^{6}(x) + cos^{6}(x))^{2}ln{10}} - \frac{96sin^{5}(x)cos(x)}{(sin^{6}(x) + cos^{6}(x))ln{10}} + \frac{540sin^{3}(x)cos^{9}(x)}{(sin^{6}(x) + cos^{6}(x))^{2}ln{10}} - \frac{432sin^{3}(x)cos^{15}(x)}{(sin^{6}(x) + cos^{6}(x))^{3}ln{10}}\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( \frac{432sin^{15}(x)cos^{3}(x)}{(sin^{6}(x) + cos^{6}(x))^{3}ln{10}} - \frac{1296sin^{11}(x)cos^{7}(x)}{(sin^{6}(x) + cos^{6}(x))^{3}ln{10}} - \frac{540sin^{9}(x)cos^{3}(x)}{(sin^{6}(x) + cos^{6}(x))^{2}ln{10}} + \frac{108sin^{11}(x)cos(x)}{(sin^{6}(x) + cos^{6}(x))^{2}ln{10}} + \frac{1296sin^{7}(x)cos^{11}(x)}{(sin^{6}(x) + cos^{6}(x))^{3}ln{10}} + \frac{648sin^{5}(x)cos^{7}(x)}{(sin^{6}(x) + cos^{6}(x))^{2}ln{10}} - \frac{648sin^{7}(x)cos^{5}(x)}{(sin^{6}(x) + cos^{6}(x))^{2}ln{10}} + \frac{96sin(x)cos^{5}(x)}{(sin^{6}(x) + cos^{6}(x))ln{10}} - \frac{108sin(x)cos^{11}(x)}{(sin^{6}(x) + cos^{6}(x))^{2}ln{10}} - \frac{96sin^{5}(x)cos(x)}{(sin^{6}(x) + cos^{6}(x))ln{10}} + \frac{540sin^{3}(x)cos^{9}(x)}{(sin^{6}(x) + cos^{6}(x))^{2}ln{10}} - \frac{432sin^{3}(x)cos^{15}(x)}{(sin^{6}(x) + cos^{6}(x))^{3}ln{10}}\right)}{dx}\\=&\frac{432(\frac{-3(6sin^{5}(x)cos(x) + -6cos^{5}(x)sin(x))}{(sin^{6}(x) + cos^{6}(x))^{4}})sin^{15}(x)cos^{3}(x)}{ln{10}} + \frac{432*-0sin^{15}(x)cos^{3}(x)}{(sin^{6}(x) + cos^{6}(x))^{3}ln^{2}{10}} + \frac{432*15sin^{14}(x)cos(x)cos^{3}(x)}{(sin^{6}(x) + cos^{6}(x))^{3}ln{10}} + \frac{432sin^{15}(x)*-3cos^{2}(x)sin(x)}{(sin^{6}(x) + cos^{6}(x))^{3}ln{10}} - \frac{1296(\frac{-3(6sin^{5}(x)cos(x) + -6cos^{5}(x)sin(x))}{(sin^{6}(x) + cos^{6}(x))^{4}})sin^{11}(x)cos^{7}(x)}{ln{10}} - \frac{1296*-0sin^{11}(x)cos^{7}(x)}{(sin^{6}(x) + cos^{6}(x))^{3}ln^{2}{10}} - \frac{1296*11sin^{10}(x)cos(x)cos^{7}(x)}{(sin^{6}(x) + cos^{6}(x))^{3}ln{10}} - \frac{1296sin^{11}(x)*-7cos^{6}(x)sin(x)}{(sin^{6}(x) + cos^{6}(x))^{3}ln{10}} - \frac{540(\frac{-2(6sin^{5}(x)cos(x) + -6cos^{5}(x)sin(x))}{(sin^{6}(x) + cos^{6}(x))^{3}})sin^{9}(x)cos^{3}(x)}{ln{10}} - \frac{540*-0sin^{9}(x)cos^{3}(x)}{(sin^{6}(x) + cos^{6}(x))^{2}ln^{2}{10}} - \frac{540*9sin^{8}(x)cos(x)cos^{3}(x)}{(sin^{6}(x) + cos^{6}(x))^{2}ln{10}} - \frac{540sin^{9}(x)*-3cos^{2}(x)sin(x)}{(sin^{6}(x) + cos^{6}(x))^{2}ln{10}} + \frac{108(\frac{-2(6sin^{5}(x)cos(x) + -6cos^{5}(x)sin(x))}{(sin^{6}(x) + cos^{6}(x))^{3}})sin^{11}(x)cos(x)}{ln{10}} + \frac{108*-0sin^{11}(x)cos(x)}{(sin^{6}(x) + cos^{6}(x))^{2}ln^{2}{10}} + \frac{108*11sin^{10}(x)cos(x)cos(x)}{(sin^{6}(x) + cos^{6}(x))^{2}ln{10}} + \frac{108sin^{11}(x)*-sin(x)}{(sin^{6}(x) + cos^{6}(x))^{2}ln{10}} + \frac{1296(\frac{-3(6sin^{5}(x)cos(x) + -6cos^{5}(x)sin(x))}{(sin^{6}(x) + cos^{6}(x))^{4}})sin^{7}(x)cos^{11}(x)}{ln{10}} + \frac{1296*-0sin^{7}(x)cos^{11}(x)}{(sin^{6}(x) + cos^{6}(x))^{3}ln^{2}{10}} + \frac{1296*7sin^{6}(x)cos(x)cos^{11}(x)}{(sin^{6}(x) + cos^{6}(x))^{3}ln{10}} + \frac{1296sin^{7}(x)*-11cos^{10}(x)sin(x)}{(sin^{6}(x) + cos^{6}(x))^{3}ln{10}} + \frac{648(\frac{-2(6sin^{5}(x)cos(x) + -6cos^{5}(x)sin(x))}{(sin^{6}(x) + cos^{6}(x))^{3}})sin^{5}(x)cos^{7}(x)}{ln{10}} + \frac{648*-0sin^{5}(x)cos^{7}(x)}{(sin^{6}(x) + cos^{6}(x))^{2}ln^{2}{10}} + \frac{648*5sin^{4}(x)cos(x)cos^{7}(x)}{(sin^{6}(x) + cos^{6}(x))^{2}ln{10}} + \frac{648sin^{5}(x)*-7cos^{6}(x)sin(x)}{(sin^{6}(x) + cos^{6}(x))^{2}ln{10}} - \frac{648(\frac{-2(6sin^{5}(x)cos(x) + -6cos^{5}(x)sin(x))}{(sin^{6}(x) + cos^{6}(x))^{3}})sin^{7}(x)cos^{5}(x)}{ln{10}} - \frac{648*-0sin^{7}(x)cos^{5}(x)}{(sin^{6}(x) + cos^{6}(x))^{2}ln^{2}{10}} - \frac{648*7sin^{6}(x)cos(x)cos^{5}(x)}{(sin^{6}(x) + cos^{6}(x))^{2}ln{10}} - \frac{648sin^{7}(x)*-5cos^{4}(x)sin(x)}{(sin^{6}(x) + cos^{6}(x))^{2}ln{10}} + \frac{96(\frac{-(6sin^{5}(x)cos(x) + -6cos^{5}(x)sin(x))}{(sin^{6}(x) + cos^{6}(x))^{2}})sin(x)cos^{5}(x)}{ln{10}} + \frac{96*-0sin(x)cos^{5}(x)}{(sin^{6}(x) + cos^{6}(x))ln^{2}{10}} + \frac{96cos(x)cos^{5}(x)}{(sin^{6}(x) + cos^{6}(x))ln{10}} + \frac{96sin(x)*-5cos^{4}(x)sin(x)}{(sin^{6}(x) + cos^{6}(x))ln{10}} - \frac{108(\frac{-2(6sin^{5}(x)cos(x) + -6cos^{5}(x)sin(x))}{(sin^{6}(x) + cos^{6}(x))^{3}})sin(x)cos^{11}(x)}{ln{10}} - \frac{108*-0sin(x)cos^{11}(x)}{(sin^{6}(x) + cos^{6}(x))^{2}ln^{2}{10}} - \frac{108cos(x)cos^{11}(x)}{(sin^{6}(x) + cos^{6}(x))^{2}ln{10}} - \frac{108sin(x)*-11cos^{10}(x)sin(x)}{(sin^{6}(x) + cos^{6}(x))^{2}ln{10}} - \frac{96(\frac{-(6sin^{5}(x)cos(x) + -6cos^{5}(x)sin(x))}{(sin^{6}(x) + cos^{6}(x))^{2}})sin^{5}(x)cos(x)}{ln{10}} - \frac{96*-0sin^{5}(x)cos(x)}{(sin^{6}(x) + cos^{6}(x))ln^{2}{10}} - \frac{96*5sin^{4}(x)cos(x)cos(x)}{(sin^{6}(x) + cos^{6}(x))ln{10}} - \frac{96sin^{5}(x)*-sin(x)}{(sin^{6}(x) + cos^{6}(x))ln{10}} + \frac{540(\frac{-2(6sin^{5}(x)cos(x) + -6cos^{5}(x)sin(x))}{(sin^{6}(x) + cos^{6}(x))^{3}})sin^{3}(x)cos^{9}(x)}{ln{10}} + \frac{540*-0sin^{3}(x)cos^{9}(x)}{(sin^{6}(x) + cos^{6}(x))^{2}ln^{2}{10}} + \frac{540*3sin^{2}(x)cos(x)cos^{9}(x)}{(sin^{6}(x) + cos^{6}(x))^{2}ln{10}} + \frac{540sin^{3}(x)*-9cos^{8}(x)sin(x)}{(sin^{6}(x) + cos^{6}(x))^{2}ln{10}} - \frac{432(\frac{-3(6sin^{5}(x)cos(x) + -6cos^{5}(x)sin(x))}{(sin^{6}(x) + cos^{6}(x))^{4}})sin^{3}(x)cos^{15}(x)}{ln{10}} - \frac{432*-0sin^{3}(x)cos^{15}(x)}{(sin^{6}(x) + cos^{6}(x))^{3}ln^{2}{10}} - \frac{432*3sin^{2}(x)cos(x)cos^{15}(x)}{(sin^{6}(x) + cos^{6}(x))^{3}ln{10}} - \frac{432sin^{3}(x)*-15cos^{14}(x)sin(x)}{(sin^{6}(x) + cos^{6}(x))^{3}ln{10}}\\=&\frac{-7776sin^{20}(x)cos^{4}(x)}{(sin^{6}(x) + cos^{6}(x))^{4}ln{10}} + \frac{31104sin^{16}(x)cos^{8}(x)}{(sin^{6}(x) + cos^{6}(x))^{4}ln{10}} + \frac{12960sin^{14}(x)cos^{4}(x)}{(sin^{6}(x) + cos^{6}(x))^{3}ln{10}} - \frac{2592sin^{16}(x)cos^{2}(x)}{(sin^{6}(x) + cos^{6}(x))^{3}ln{10}} - \frac{46656sin^{12}(x)cos^{12}(x)}{(sin^{6}(x) + cos^{6}(x))^{4}ln{10}} - \frac{28512sin^{10}(x)cos^{8}(x)}{(sin^{6}(x) + cos^{6}(x))^{3}ln{10}} - \frac{1620sin^{8}(x)cos^{4}(x)}{(sin^{6}(x) + cos^{6}(x))^{2}ln{10}} + \frac{18144sin^{12}(x)cos^{6}(x)}{(sin^{6}(x) + cos^{6}(x))^{3}ln{10}} + \frac{3384sin^{10}(x)cos^{2}(x)}{(sin^{6}(x) + cos^{6}(x))^{2}ln{10}} + \frac{18144sin^{6}(x)cos^{12}(x)}{(sin^{6}(x) + cos^{6}(x))^{3}ln{10}} - \frac{1620sin^{4}(x)cos^{8}(x)}{(sin^{6}(x) + cos^{6}(x))^{2}ln{10}} - \frac{10224sin^{6}(x)cos^{6}(x)}{(sin^{6}(x) + cos^{6}(x))^{2}ln{10}} - \frac{28512sin^{8}(x)cos^{10}(x)}{(sin^{6}(x) + cos^{6}(x))^{3}ln{10}} + \frac{31104sin^{8}(x)cos^{16}(x)}{(sin^{6}(x) + cos^{6}(x))^{4}ln{10}} - \frac{480sin^{4}(x)cos^{2}(x)}{(sin^{6}(x) + cos^{6}(x))ln{10}} + \frac{3384sin^{2}(x)cos^{10}(x)}{(sin^{6}(x) + cos^{6}(x))^{2}ln{10}} - \frac{2592sin^{2}(x)cos^{16}(x)}{(sin^{6}(x) + cos^{6}(x))^{3}ln{10}} - \frac{480sin^{2}(x)cos^{4}(x)}{(sin^{6}(x) + cos^{6}(x))ln{10}} + \frac{96cos^{6}(x)}{(sin^{6}(x) + cos^{6}(x))ln{10}} - \frac{108cos^{12}(x)}{(sin^{6}(x) + cos^{6}(x))^{2}ln{10}} + \frac{12960sin^{4}(x)cos^{14}(x)}{(sin^{6}(x) + cos^{6}(x))^{3}ln{10}} - \frac{7776sin^{4}(x)cos^{20}(x)}{(sin^{6}(x) + cos^{6}(x))^{4}ln{10}} - \frac{108sin^{12}(x)}{(sin^{6}(x) + cos^{6}(x))^{2}ln{10}} + \frac{96sin^{6}(x)}{(sin^{6}(x) + cos^{6}(x))ln{10}}\\ \end{split}\end{equation} \]
注意，变量是区分大小写的。
\[ \begin{equation}\begin{split}【1/1】求函数lg({(sin(x))}^{6} + {(cos(x))}^{6}) 关于 x 的 4 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = lg(sin^{6}(x) + cos^{6}(x))\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( lg(sin^{6}(x) + cos^{6}(x))\right)}{dx}\\=&\frac{(6sin^{5}(x)cos(x) + -6cos^{5}(x)sin(x))}{ln{10}(sin^{6}(x) + cos^{6}(x))}\\=&\frac{6sin^{5}(x)cos(x)}{(sin^{6}(x) + cos^{6}(x))ln{10}} - \frac{6sin(x)cos^{5}(x)}{(sin^{6}(x) + cos^{6}(x))ln{10}}\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( \frac{6sin^{5}(x)cos(x)}{(sin^{6}(x) + cos^{6}(x))ln{10}} - \frac{6sin(x)cos^{5}(x)}{(sin^{6}(x) + cos^{6}(x))ln{10}}\right)}{dx}\\=&\frac{6(\frac{-(6sin^{5}(x)cos(x) + -6cos^{5}(x)sin(x))}{(sin^{6}(x) + cos^{6}(x))^{2}})sin^{5}(x)cos(x)}{ln{10}} + \frac{6*-0sin^{5}(x)cos(x)}{(sin^{6}(x) + cos^{6}(x))ln^{2}{10}} + \frac{6*5sin^{4}(x)cos(x)cos(x)}{(sin^{6}(x) + cos^{6}(x))ln{10}} + \frac{6sin^{5}(x)*-sin(x)}{(sin^{6}(x) + cos^{6}(x))ln{10}} - \frac{6(\frac{-(6sin^{5}(x)cos(x) + -6cos^{5}(x)sin(x))}{(sin^{6}(x) + cos^{6}(x))^{2}})sin(x)cos^{5}(x)}{ln{10}} - \frac{6*-0sin(x)cos^{5}(x)}{(sin^{6}(x) + cos^{6}(x))ln^{2}{10}} - \frac{6cos(x)cos^{5}(x)}{(sin^{6}(x) + cos^{6}(x))ln{10}} - \frac{6sin(x)*-5cos^{4}(x)sin(x)}{(sin^{6}(x) + cos^{6}(x))ln{10}}\\=&\frac{-36sin^{10}(x)cos^{2}(x)}{(sin^{6}(x) + cos^{6}(x))^{2}ln{10}} + \frac{72sin^{6}(x)cos^{6}(x)}{(sin^{6}(x) + cos^{6}(x))^{2}ln{10}} + \frac{30sin^{4}(x)cos^{2}(x)}{(sin^{6}(x) + cos^{6}(x))ln{10}} + \frac{30sin^{2}(x)cos^{4}(x)}{(sin^{6}(x) + cos^{6}(x))ln{10}} - \frac{36sin^{2}(x)cos^{10}(x)}{(sin^{6}(x) + cos^{6}(x))^{2}ln{10}} - \frac{6cos^{6}(x)}{(sin^{6}(x) + cos^{6}(x))ln{10}} - \frac{6sin^{6}(x)}{(sin^{6}(x) + cos^{6}(x))ln{10}}\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( \frac{-36sin^{10}(x)cos^{2}(x)}{(sin^{6}(x) + cos^{6}(x))^{2}ln{10}} + \frac{72sin^{6}(x)cos^{6}(x)}{(sin^{6}(x) + cos^{6}(x))^{2}ln{10}} + \frac{30sin^{4}(x)cos^{2}(x)}{(sin^{6}(x) + cos^{6}(x))ln{10}} + \frac{30sin^{2}(x)cos^{4}(x)}{(sin^{6}(x) + cos^{6}(x))ln{10}} - \frac{36sin^{2}(x)cos^{10}(x)}{(sin^{6}(x) + cos^{6}(x))^{2}ln{10}} - \frac{6cos^{6}(x)}{(sin^{6}(x) + cos^{6}(x))ln{10}} - \frac{6sin^{6}(x)}{(sin^{6}(x) + cos^{6}(x))ln{10}}\right)}{dx}\\=&\frac{-36(\frac{-2(6sin^{5}(x)cos(x) + -6cos^{5}(x)sin(x))}{(sin^{6}(x) + cos^{6}(x))^{3}})sin^{10}(x)cos^{2}(x)}{ln{10}} - \frac{36*-0sin^{10}(x)cos^{2}(x)}{(sin^{6}(x) + cos^{6}(x))^{2}ln^{2}{10}} - \frac{36*10sin^{9}(x)cos(x)cos^{2}(x)}{(sin^{6}(x) + cos^{6}(x))^{2}ln{10}} - \frac{36sin^{10}(x)*-2cos(x)sin(x)}{(sin^{6}(x) + cos^{6}(x))^{2}ln{10}} + \frac{72(\frac{-2(6sin^{5}(x)cos(x) + -6cos^{5}(x)sin(x))}{(sin^{6}(x) + cos^{6}(x))^{3}})sin^{6}(x)cos^{6}(x)}{ln{10}} + \frac{72*-0sin^{6}(x)cos^{6}(x)}{(sin^{6}(x) + cos^{6}(x))^{2}ln^{2}{10}} + \frac{72*6sin^{5}(x)cos(x)cos^{6}(x)}{(sin^{6}(x) + cos^{6}(x))^{2}ln{10}} + \frac{72sin^{6}(x)*-6cos^{5}(x)sin(x)}{(sin^{6}(x) + cos^{6}(x))^{2}ln{10}} + \frac{30(\frac{-(6sin^{5}(x)cos(x) + -6cos^{5}(x)sin(x))}{(sin^{6}(x) + cos^{6}(x))^{2}})sin^{4}(x)cos^{2}(x)}{ln{10}} + \frac{30*-0sin^{4}(x)cos^{2}(x)}{(sin^{6}(x) + cos^{6}(x))ln^{2}{10}} + \frac{30*4sin^{3}(x)cos(x)cos^{2}(x)}{(sin^{6}(x) + cos^{6}(x))ln{10}} + \frac{30sin^{4}(x)*-2cos(x)sin(x)}{(sin^{6}(x) + cos^{6}(x))ln{10}} + \frac{30(\frac{-(6sin^{5}(x)cos(x) + -6cos^{5}(x)sin(x))}{(sin^{6}(x) + cos^{6}(x))^{2}})sin^{2}(x)cos^{4}(x)}{ln{10}} + \frac{30*-0sin^{2}(x)cos^{4}(x)}{(sin^{6}(x) + cos^{6}(x))ln^{2}{10}} + \frac{30*2sin(x)cos(x)cos^{4}(x)}{(sin^{6}(x) + cos^{6}(x))ln{10}} + \frac{30sin^{2}(x)*-4cos^{3}(x)sin(x)}{(sin^{6}(x) + cos^{6}(x))ln{10}} - \frac{36(\frac{-2(6sin^{5}(x)cos(x) + -6cos^{5}(x)sin(x))}{(sin^{6}(x) + cos^{6}(x))^{3}})sin^{2}(x)cos^{10}(x)}{ln{10}} - \frac{36*-0sin^{2}(x)cos^{10}(x)}{(sin^{6}(x) + cos^{6}(x))^{2}ln^{2}{10}} - \frac{36*2sin(x)cos(x)cos^{10}(x)}{(sin^{6}(x) + cos^{6}(x))^{2}ln{10}} - \frac{36sin^{2}(x)*-10cos^{9}(x)sin(x)}{(sin^{6}(x) + cos^{6}(x))^{2}ln{10}} - \frac{6(\frac{-(6sin^{5}(x)cos(x) + -6cos^{5}(x)sin(x))}{(sin^{6}(x) + cos^{6}(x))^{2}})cos^{6}(x)}{ln{10}} - \frac{6*-0cos^{6}(x)}{(sin^{6}(x) + cos^{6}(x))ln^{2}{10}} - \frac{6*-6cos^{5}(x)sin(x)}{(sin^{6}(x) + cos^{6}(x))ln{10}} - \frac{6(\frac{-(6sin^{5}(x)cos(x) + -6cos^{5}(x)sin(x))}{(sin^{6}(x) + cos^{6}(x))^{2}})sin^{6}(x)}{ln{10}} - \frac{6*-0sin^{6}(x)}{(sin^{6}(x) + cos^{6}(x))ln^{2}{10}} - \frac{6*6sin^{5}(x)cos(x)}{(sin^{6}(x) + cos^{6}(x))ln{10}}\\=&\frac{432sin^{15}(x)cos^{3}(x)}{(sin^{6}(x) + cos^{6}(x))^{3}ln{10}} - \frac{1296sin^{11}(x)cos^{7}(x)}{(sin^{6}(x) + cos^{6}(x))^{3}ln{10}} - \frac{540sin^{9}(x)cos^{3}(x)}{(sin^{6}(x) + cos^{6}(x))^{2}ln{10}} + \frac{108sin^{11}(x)cos(x)}{(sin^{6}(x) + cos^{6}(x))^{2}ln{10}} + \frac{1296sin^{7}(x)cos^{11}(x)}{(sin^{6}(x) + cos^{6}(x))^{3}ln{10}} + \frac{648sin^{5}(x)cos^{7}(x)}{(sin^{6}(x) + cos^{6}(x))^{2}ln{10}} - \frac{648sin^{7}(x)cos^{5}(x)}{(sin^{6}(x) + cos^{6}(x))^{2}ln{10}} + \frac{96sin(x)cos^{5}(x)}{(sin^{6}(x) + cos^{6}(x))ln{10}} - \frac{108sin(x)cos^{11}(x)}{(sin^{6}(x) + cos^{6}(x))^{2}ln{10}} - \frac{96sin^{5}(x)cos(x)}{(sin^{6}(x) + cos^{6}(x))ln{10}} + \frac{540sin^{3}(x)cos^{9}(x)}{(sin^{6}(x) + cos^{6}(x))^{2}ln{10}} - \frac{432sin^{3}(x)cos^{15}(x)}{(sin^{6}(x) + cos^{6}(x))^{3}ln{10}}\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( \frac{432sin^{15}(x)cos^{3}(x)}{(sin^{6}(x) + cos^{6}(x))^{3}ln{10}} - \frac{1296sin^{11}(x)cos^{7}(x)}{(sin^{6}(x) + cos^{6}(x))^{3}ln{10}} - \frac{540sin^{9}(x)cos^{3}(x)}{(sin^{6}(x) + cos^{6}(x))^{2}ln{10}} + \frac{108sin^{11}(x)cos(x)}{(sin^{6}(x) + cos^{6}(x))^{2}ln{10}} + \frac{1296sin^{7}(x)cos^{11}(x)}{(sin^{6}(x) + cos^{6}(x))^{3}ln{10}} + \frac{648sin^{5}(x)cos^{7}(x)}{(sin^{6}(x) + cos^{6}(x))^{2}ln{10}} - \frac{648sin^{7}(x)cos^{5}(x)}{(sin^{6}(x) + cos^{6}(x))^{2}ln{10}} + \frac{96sin(x)cos^{5}(x)}{(sin^{6}(x) + cos^{6}(x))ln{10}} - \frac{108sin(x)cos^{11}(x)}{(sin^{6}(x) + cos^{6}(x))^{2}ln{10}} - \frac{96sin^{5}(x)cos(x)}{(sin^{6}(x) + cos^{6}(x))ln{10}} + \frac{540sin^{3}(x)cos^{9}(x)}{(sin^{6}(x) + cos^{6}(x))^{2}ln{10}} - \frac{432sin^{3}(x)cos^{15}(x)}{(sin^{6}(x) + cos^{6}(x))^{3}ln{10}}\right)}{dx}\\=&\frac{432(\frac{-3(6sin^{5}(x)cos(x) + -6cos^{5}(x)sin(x))}{(sin^{6}(x) + cos^{6}(x))^{4}})sin^{15}(x)cos^{3}(x)}{ln{10}} + \frac{432*-0sin^{15}(x)cos^{3}(x)}{(sin^{6}(x) + cos^{6}(x))^{3}ln^{2}{10}} + \frac{432*15sin^{14}(x)cos(x)cos^{3}(x)}{(sin^{6}(x) + cos^{6}(x))^{3}ln{10}} + \frac{432sin^{15}(x)*-3cos^{2}(x)sin(x)}{(sin^{6}(x) + cos^{6}(x))^{3}ln{10}} - \frac{1296(\frac{-3(6sin^{5}(x)cos(x) + -6cos^{5}(x)sin(x))}{(sin^{6}(x) + cos^{6}(x))^{4}})sin^{11}(x)cos^{7}(x)}{ln{10}} - \frac{1296*-0sin^{11}(x)cos^{7}(x)}{(sin^{6}(x) + cos^{6}(x))^{3}ln^{2}{10}} - \frac{1296*11sin^{10}(x)cos(x)cos^{7}(x)}{(sin^{6}(x) + cos^{6}(x))^{3}ln{10}} - \frac{1296sin^{11}(x)*-7cos^{6}(x)sin(x)}{(sin^{6}(x) + cos^{6}(x))^{3}ln{10}} - \frac{540(\frac{-2(6sin^{5}(x)cos(x) + -6cos^{5}(x)sin(x))}{(sin^{6}(x) + cos^{6}(x))^{3}})sin^{9}(x)cos^{3}(x)}{ln{10}} - \frac{540*-0sin^{9}(x)cos^{3}(x)}{(sin^{6}(x) + cos^{6}(x))^{2}ln^{2}{10}} - \frac{540*9sin^{8}(x)cos(x)cos^{3}(x)}{(sin^{6}(x) + cos^{6}(x))^{2}ln{10}} - \frac{540sin^{9}(x)*-3cos^{2}(x)sin(x)}{(sin^{6}(x) + cos^{6}(x))^{2}ln{10}} + \frac{108(\frac{-2(6sin^{5}(x)cos(x) + -6cos^{5}(x)sin(x))}{(sin^{6}(x) + cos^{6}(x))^{3}})sin^{11}(x)cos(x)}{ln{10}} + \frac{108*-0sin^{11}(x)cos(x)}{(sin^{6}(x) + cos^{6}(x))^{2}ln^{2}{10}} + \frac{108*11sin^{10}(x)cos(x)cos(x)}{(sin^{6}(x) + cos^{6}(x))^{2}ln{10}} + \frac{108sin^{11}(x)*-sin(x)}{(sin^{6}(x) + cos^{6}(x))^{2}ln{10}} + \frac{1296(\frac{-3(6sin^{5}(x)cos(x) + -6cos^{5}(x)sin(x))}{(sin^{6}(x) + cos^{6}(x))^{4}})sin^{7}(x)cos^{11}(x)}{ln{10}} + \frac{1296*-0sin^{7}(x)cos^{11}(x)}{(sin^{6}(x) + cos^{6}(x))^{3}ln^{2}{10}} + \frac{1296*7sin^{6}(x)cos(x)cos^{11}(x)}{(sin^{6}(x) + cos^{6}(x))^{3}ln{10}} + \frac{1296sin^{7}(x)*-11cos^{10}(x)sin(x)}{(sin^{6}(x) + cos^{6}(x))^{3}ln{10}} + \frac{648(\frac{-2(6sin^{5}(x)cos(x) + -6cos^{5}(x)sin(x))}{(sin^{6}(x) + cos^{6}(x))^{3}})sin^{5}(x)cos^{7}(x)}{ln{10}} + \frac{648*-0sin^{5}(x)cos^{7}(x)}{(sin^{6}(x) + cos^{6}(x))^{2}ln^{2}{10}} + \frac{648*5sin^{4}(x)cos(x)cos^{7}(x)}{(sin^{6}(x) + cos^{6}(x))^{2}ln{10}} + \frac{648sin^{5}(x)*-7cos^{6}(x)sin(x)}{(sin^{6}(x) + cos^{6}(x))^{2}ln{10}} - \frac{648(\frac{-2(6sin^{5}(x)cos(x) + -6cos^{5}(x)sin(x))}{(sin^{6}(x) + cos^{6}(x))^{3}})sin^{7}(x)cos^{5}(x)}{ln{10}} - \frac{648*-0sin^{7}(x)cos^{5}(x)}{(sin^{6}(x) + cos^{6}(x))^{2}ln^{2}{10}} - \frac{648*7sin^{6}(x)cos(x)cos^{5}(x)}{(sin^{6}(x) + cos^{6}(x))^{2}ln{10}} - \frac{648sin^{7}(x)*-5cos^{4}(x)sin(x)}{(sin^{6}(x) + cos^{6}(x))^{2}ln{10}} + \frac{96(\frac{-(6sin^{5}(x)cos(x) + -6cos^{5}(x)sin(x))}{(sin^{6}(x) + cos^{6}(x))^{2}})sin(x)cos^{5}(x)}{ln{10}} + \frac{96*-0sin(x)cos^{5}(x)}{(sin^{6}(x) + cos^{6}(x))ln^{2}{10}} + \frac{96cos(x)cos^{5}(x)}{(sin^{6}(x) + cos^{6}(x))ln{10}} + \frac{96sin(x)*-5cos^{4}(x)sin(x)}{(sin^{6}(x) + cos^{6}(x))ln{10}} - \frac{108(\frac{-2(6sin^{5}(x)cos(x) + -6cos^{5}(x)sin(x))}{(sin^{6}(x) + cos^{6}(x))^{3}})sin(x)cos^{11}(x)}{ln{10}} - \frac{108*-0sin(x)cos^{11}(x)}{(sin^{6}(x) + cos^{6}(x))^{2}ln^{2}{10}} - \frac{108cos(x)cos^{11}(x)}{(sin^{6}(x) + cos^{6}(x))^{2}ln{10}} - \frac{108sin(x)*-11cos^{10}(x)sin(x)}{(sin^{6}(x) + cos^{6}(x))^{2}ln{10}} - \frac{96(\frac{-(6sin^{5}(x)cos(x) + -6cos^{5}(x)sin(x))}{(sin^{6}(x) + cos^{6}(x))^{2}})sin^{5}(x)cos(x)}{ln{10}} - \frac{96*-0sin^{5}(x)cos(x)}{(sin^{6}(x) + cos^{6}(x))ln^{2}{10}} - \frac{96*5sin^{4}(x)cos(x)cos(x)}{(sin^{6}(x) + cos^{6}(x))ln{10}} - \frac{96sin^{5}(x)*-sin(x)}{(sin^{6}(x) + cos^{6}(x))ln{10}} + \frac{540(\frac{-2(6sin^{5}(x)cos(x) + -6cos^{5}(x)sin(x))}{(sin^{6}(x) + cos^{6}(x))^{3}})sin^{3}(x)cos^{9}(x)}{ln{10}} + \frac{540*-0sin^{3}(x)cos^{9}(x)}{(sin^{6}(x) + cos^{6}(x))^{2}ln^{2}{10}} + \frac{540*3sin^{2}(x)cos(x)cos^{9}(x)}{(sin^{6}(x) + cos^{6}(x))^{2}ln{10}} + \frac{540sin^{3}(x)*-9cos^{8}(x)sin(x)}{(sin^{6}(x) + cos^{6}(x))^{2}ln{10}} - \frac{432(\frac{-3(6sin^{5}(x)cos(x) + -6cos^{5}(x)sin(x))}{(sin^{6}(x) + cos^{6}(x))^{4}})sin^{3}(x)cos^{15}(x)}{ln{10}} - \frac{432*-0sin^{3}(x)cos^{15}(x)}{(sin^{6}(x) + cos^{6}(x))^{3}ln^{2}{10}} - \frac{432*3sin^{2}(x)cos(x)cos^{15}(x)}{(sin^{6}(x) + cos^{6}(x))^{3}ln{10}} - \frac{432sin^{3}(x)*-15cos^{14}(x)sin(x)}{(sin^{6}(x) + cos^{6}(x))^{3}ln{10}}\\=&\frac{-7776sin^{20}(x)cos^{4}(x)}{(sin^{6}(x) + cos^{6}(x))^{4}ln{10}} + \frac{31104sin^{16}(x)cos^{8}(x)}{(sin^{6}(x) + cos^{6}(x))^{4}ln{10}} + \frac{12960sin^{14}(x)cos^{4}(x)}{(sin^{6}(x) + cos^{6}(x))^{3}ln{10}} - \frac{2592sin^{16}(x)cos^{2}(x)}{(sin^{6}(x) + cos^{6}(x))^{3}ln{10}} - \frac{46656sin^{12}(x)cos^{12}(x)}{(sin^{6}(x) + cos^{6}(x))^{4}ln{10}} - \frac{28512sin^{10}(x)cos^{8}(x)}{(sin^{6}(x) + cos^{6}(x))^{3}ln{10}} - \frac{1620sin^{8}(x)cos^{4}(x)}{(sin^{6}(x) + cos^{6}(x))^{2}ln{10}} + \frac{18144sin^{12}(x)cos^{6}(x)}{(sin^{6}(x) + cos^{6}(x))^{3}ln{10}} + \frac{3384sin^{10}(x)cos^{2}(x)}{(sin^{6}(x) + cos^{6}(x))^{2}ln{10}} + \frac{18144sin^{6}(x)cos^{12}(x)}{(sin^{6}(x) + cos^{6}(x))^{3}ln{10}} - \frac{1620sin^{4}(x)cos^{8}(x)}{(sin^{6}(x) + cos^{6}(x))^{2}ln{10}} - \frac{10224sin^{6}(x)cos^{6}(x)}{(sin^{6}(x) + cos^{6}(x))^{2}ln{10}} - \frac{28512sin^{8}(x)cos^{10}(x)}{(sin^{6}(x) + cos^{6}(x))^{3}ln{10}} + \frac{31104sin^{8}(x)cos^{16}(x)}{(sin^{6}(x) + cos^{6}(x))^{4}ln{10}} - \frac{480sin^{4}(x)cos^{2}(x)}{(sin^{6}(x) + cos^{6}(x))ln{10}} + \frac{3384sin^{2}(x)cos^{10}(x)}{(sin^{6}(x) + cos^{6}(x))^{2}ln{10}} - \frac{2592sin^{2}(x)cos^{16}(x)}{(sin^{6}(x) + cos^{6}(x))^{3}ln{10}} - \frac{480sin^{2}(x)cos^{4}(x)}{(sin^{6}(x) + cos^{6}(x))ln{10}} + \frac{96cos^{6}(x)}{(sin^{6}(x) + cos^{6}(x))ln{10}} - \frac{108cos^{12}(x)}{(sin^{6}(x) + cos^{6}(x))^{2}ln{10}} + \frac{12960sin^{4}(x)cos^{14}(x)}{(sin^{6}(x) + cos^{6}(x))^{3}ln{10}} - \frac{7776sin^{4}(x)cos^{20}(x)}{(sin^{6}(x) + cos^{6}(x))^{4}ln{10}} - \frac{108sin^{12}(x)}{(sin^{6}(x) + cos^{6}(x))^{2}ln{10}} + \frac{96sin^{6}(x)}{(sin^{6}(x) + cos^{6}(x))ln{10}}\\ \end{split}\end{equation} \]
你的问题在这里没有得到解决？请到 热门难题 里面看看吧！
最 新 发 布
新增加身体健康评估计算器，位置：“数学运算 > 身体健康评估”。
新增加学习笔记(安卓版)百度网盘快速下载应用程序，欢迎使用。
新增加学习笔记(安卓版)本站下载应用程序，欢迎使用。
新增线性代数行列式的计算，欢迎使用。
数学计算和一元方程已经支持正割函数和余割函数，欢迎使用。
新增加贷款计算器模块（具体位置：数学运算 > 贷款计算器），欢迎使用。