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 5 个题目：每一题对 x 求 4 阶导数。
注意，变量是区分大小写的。
\[ \begin{equation}\begin{split}【1/5】求函数lg(lg(x)) 关于 x 的 4 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( lg(lg(x))\right)}{dx}\\=&\frac{1}{ln{10}(lg(x))ln{10}(x)}\\=&\frac{1}{xln^{2}{10}lg(x)}\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( \frac{1}{xln^{2}{10}lg(x)}\right)}{dx}\\=&\frac{-1}{x^{2}ln^{2}{10}lg(x)} + \frac{-2*0}{xln^{3}{10}lg(x)} + \frac{-1}{xln^{2}{10}lg^{2}(x)ln{10}(x)}\\=&\frac{-1}{x^{2}ln^{2}{10}lg(x)} - \frac{1}{x^{2}ln^{3}{10}lg^{2}(x)}\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( \frac{-1}{x^{2}ln^{2}{10}lg(x)} - \frac{1}{x^{2}ln^{3}{10}lg^{2}(x)}\right)}{dx}\\=&\frac{--2}{x^{3}ln^{2}{10}lg(x)} - \frac{-2*0}{x^{2}ln^{3}{10}lg(x)} - \frac{-1}{x^{2}ln^{2}{10}lg^{2}(x)ln{10}(x)} - \frac{-2}{x^{3}ln^{3}{10}lg^{2}(x)} - \frac{-3*0}{x^{2}ln^{4}{10}lg^{2}(x)} - \frac{-2}{x^{2}ln^{3}{10}lg^{3}(x)ln{10}(x)}\\=&\frac{2}{x^{3}ln^{2}{10}lg(x)} + \frac{3}{x^{3}ln^{3}{10}lg^{2}(x)} + \frac{2}{x^{3}ln^{4}{10}lg^{3}(x)}\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( \frac{2}{x^{3}ln^{2}{10}lg(x)} + \frac{3}{x^{3}ln^{3}{10}lg^{2}(x)} + \frac{2}{x^{3}ln^{4}{10}lg^{3}(x)}\right)}{dx}\\=&\frac{2*-3}{x^{4}ln^{2}{10}lg(x)} + \frac{2*-2*0}{x^{3}ln^{3}{10}lg(x)} + \frac{2*-1}{x^{3}ln^{2}{10}lg^{2}(x)ln{10}(x)} + \frac{3*-3}{x^{4}ln^{3}{10}lg^{2}(x)} + \frac{3*-3*0}{x^{3}ln^{4}{10}lg^{2}(x)} + \frac{3*-2}{x^{3}ln^{3}{10}lg^{3}(x)ln{10}(x)} + \frac{2*-3}{x^{4}ln^{4}{10}lg^{3}(x)} + \frac{2*-4*0}{x^{3}ln^{5}{10}lg^{3}(x)} + \frac{2*-3}{x^{3}ln^{4}{10}lg^{4}(x)ln{10}(x)}\\=&\frac{-6}{x^{4}ln^{2}{10}lg(x)} - \frac{11}{x^{4}ln^{3}{10}lg^{2}(x)} - \frac{12}{x^{4}ln^{4}{10}lg^{3}(x)} - \frac{6}{x^{4}ln^{5}{10}lg^{4}(x)}\\ \end{split}\end{equation} \]
\[ \begin{equation}\begin{split}【2/5】求函数ln(ln(x)) 关于 x 的 4 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( ln(ln(x))\right)}{dx}\\=&\frac{1}{(ln(x))(x)}\\=&\frac{1}{xln(x)}\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( \frac{1}{xln(x)}\right)}{dx}\\=&\frac{-1}{x^{2}ln(x)} + \frac{-1}{xln^{2}(x)(x)}\\=&\frac{-1}{x^{2}ln(x)} - \frac{1}{x^{2}ln^{2}(x)}\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( \frac{-1}{x^{2}ln(x)} - \frac{1}{x^{2}ln^{2}(x)}\right)}{dx}\\=&\frac{--2}{x^{3}ln(x)} - \frac{-1}{x^{2}ln^{2}(x)(x)} - \frac{-2}{x^{3}ln^{2}(x)} - \frac{-2}{x^{2}ln^{3}(x)(x)}\\=&\frac{2}{x^{3}ln(x)} + \frac{3}{x^{3}ln^{2}(x)} + \frac{2}{x^{3}ln^{3}(x)}\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( \frac{2}{x^{3}ln(x)} + \frac{3}{x^{3}ln^{2}(x)} + \frac{2}{x^{3}ln^{3}(x)}\right)}{dx}\\=&\frac{2*-3}{x^{4}ln(x)} + \frac{2*-1}{x^{3}ln^{2}(x)(x)} + \frac{3*-3}{x^{4}ln^{2}(x)} + \frac{3*-2}{x^{3}ln^{3}(x)(x)} + \frac{2*-3}{x^{4}ln^{3}(x)} + \frac{2*-3}{x^{3}ln^{4}(x)(x)}\\=&\frac{-6}{x^{4}ln(x)} - \frac{11}{x^{4}ln^{2}(x)} - \frac{12}{x^{4}ln^{3}(x)} - \frac{6}{x^{4}ln^{4}(x)}\\ \end{split}\end{equation} \]
\[ \begin{equation}\begin{split}【3/5】求函数sin(sin(x)) 关于 x 的 4 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( sin(sin(x))\right)}{dx}\\=&cos(sin(x))cos(x)\\=&cos(x)cos(sin(x))\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( cos(x)cos(sin(x))\right)}{dx}\\=&-sin(x)cos(sin(x)) + cos(x)*-sin(sin(x))cos(x)\\=&-sin(x)cos(sin(x)) - sin(sin(x))cos^{2}(x)\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( -sin(x)cos(sin(x)) - sin(sin(x))cos^{2}(x)\right)}{dx}\\=&-cos(x)cos(sin(x)) - sin(x)*-sin(sin(x))cos(x) - cos(sin(x))cos(x)cos^{2}(x) - sin(sin(x))*-2cos(x)sin(x)\\=&-cos(x)cos(sin(x)) + 3sin(x)sin(sin(x))cos(x) - cos^{3}(x)cos(sin(x))\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( -cos(x)cos(sin(x)) + 3sin(x)sin(sin(x))cos(x) - cos^{3}(x)cos(sin(x))\right)}{dx}\\=&--sin(x)cos(sin(x)) - cos(x)*-sin(sin(x))cos(x) + 3cos(x)sin(sin(x))cos(x) + 3sin(x)cos(sin(x))cos(x)cos(x) + 3sin(x)sin(sin(x))*-sin(x) - -3cos^{2}(x)sin(x)cos(sin(x)) - cos^{3}(x)*-sin(sin(x))cos(x)\\=&6sin(x)cos^{2}(x)cos(sin(x)) + 4sin(sin(x))cos^{2}(x) - 3sin^{2}(x)sin(sin(x)) + sin(x)cos(sin(x)) + sin(sin(x))cos^{4}(x)\\ \end{split}\end{equation} \]
\[ \begin{equation}\begin{split}【4/5】求函数cos(cos(x)) 关于 x 的 4 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( cos(cos(x))\right)}{dx}\\=&-sin(cos(x))*-sin(x)\\=&sin(x)sin(cos(x))\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( sin(x)sin(cos(x))\right)}{dx}\\=&cos(x)sin(cos(x)) + sin(x)cos(cos(x))*-sin(x)\\=&sin(cos(x))cos(x) - sin^{2}(x)cos(cos(x))\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( sin(cos(x))cos(x) - sin^{2}(x)cos(cos(x))\right)}{dx}\\=&cos(cos(x))*-sin(x)cos(x) + sin(cos(x))*-sin(x) - 2sin(x)cos(x)cos(cos(x)) - sin^{2}(x)*-sin(cos(x))*-sin(x)\\=&-sin(x)cos(cos(x))cos(x) - sin(x)sin(cos(x)) - 2sin(x)cos(x)cos(cos(x)) - sin(cos(x))sin^{3}(x)\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( -sin(x)cos(cos(x))cos(x) - sin(x)sin(cos(x)) - 2sin(x)cos(x)cos(cos(x)) - sin(cos(x))sin^{3}(x)\right)}{dx}\\=&-cos(x)cos(cos(x))cos(x) - sin(x)*-sin(cos(x))*-sin(x)cos(x) - sin(x)cos(cos(x))*-sin(x) - cos(x)sin(cos(x)) - sin(x)cos(cos(x))*-sin(x) - 2cos(x)cos(x)cos(cos(x)) - 2sin(x)*-sin(x)cos(cos(x)) - 2sin(x)cos(x)*-sin(cos(x))*-sin(x) - cos(cos(x))*-sin(x)sin^{3}(x) - sin(cos(x))*3sin^{2}(x)cos(x)\\=&-3cos^{2}(x)cos(cos(x)) - 3sin(cos(x))sin^{2}(x)cos(x) + 4sin^{2}(x)cos(cos(x)) - sin(cos(x))cos(x) + sin^{4}(x)cos(cos(x)) - 3sin^{2}(x)sin(cos(x))cos(x)\\ \end{split}\end{equation} \]
\[ \begin{equation}\begin{split}【5/5】求函数tan(tan(x)) 关于 x 的 4 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( tan(tan(x))\right)}{dx}\\=&sec^{2}(tan(x))(sec^{2}(x)(1))\\=&sec^{2}(x)sec^{2}(tan(x))\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( sec^{2}(x)sec^{2}(tan(x))\right)}{dx}\\=&2sec^{2}(x)tan(x)sec^{2}(tan(x)) + sec^{2}(x)*2sec^{2}(tan(x))tan(tan(x))sec^{2}(x)(1)\\=&2tan(x)sec^{2}(x)sec^{2}(tan(x)) + 2tan(tan(x))sec^{2}(tan(x))sec^{4}(x)\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( 2tan(x)sec^{2}(x)sec^{2}(tan(x)) + 2tan(tan(x))sec^{2}(tan(x))sec^{4}(x)\right)}{dx}\\=&2sec^{2}(x)(1)sec^{2}(x)sec^{2}(tan(x)) + 2tan(x)*2sec^{2}(x)tan(x)sec^{2}(tan(x)) + 2tan(x)sec^{2}(x)*2sec^{2}(tan(x))tan(tan(x))sec^{2}(x)(1) + 2sec^{2}(tan(x))(sec^{2}(x)(1))sec^{2}(tan(x))sec^{4}(x) + 2tan(tan(x))*2sec^{2}(tan(x))tan(tan(x))sec^{2}(x)(1)sec^{4}(x) + 2tan(tan(x))sec^{2}(tan(x))*4sec^{4}(x)tan(x)\\=&2sec^{4}(x)sec^{2}(tan(x)) + 4tan^{2}(x)sec^{2}(x)sec^{2}(tan(x)) + 12tan(x)tan(tan(x))sec^{2}(tan(x))sec^{4}(x) + 2sec^{6}(x)sec^{4}(tan(x)) + 4tan^{2}(tan(x))sec^{6}(x)sec^{2}(tan(x))\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( 2sec^{4}(x)sec^{2}(tan(x)) + 4tan^{2}(x)sec^{2}(x)sec^{2}(tan(x)) + 12tan(x)tan(tan(x))sec^{2}(tan(x))sec^{4}(x) + 2sec^{6}(x)sec^{4}(tan(x)) + 4tan^{2}(tan(x))sec^{6}(x)sec^{2}(tan(x))\right)}{dx}\\=&2*4sec^{4}(x)tan(x)sec^{2}(tan(x)) + 2sec^{4}(x)*2sec^{2}(tan(x))tan(tan(x))sec^{2}(x)(1) + 4*2tan(x)sec^{2}(x)(1)sec^{2}(x)sec^{2}(tan(x)) + 4tan^{2}(x)*2sec^{2}(x)tan(x)sec^{2}(tan(x)) + 4tan^{2}(x)sec^{2}(x)*2sec^{2}(tan(x))tan(tan(x))sec^{2}(x)(1) + 12sec^{2}(x)(1)tan(tan(x))sec^{2}(tan(x))sec^{4}(x) + 12tan(x)sec^{2}(tan(x))(sec^{2}(x)(1))sec^{2}(tan(x))sec^{4}(x) + 12tan(x)tan(tan(x))*2sec^{2}(tan(x))tan(tan(x))sec^{2}(x)(1)sec^{4}(x) + 12tan(x)tan(tan(x))sec^{2}(tan(x))*4sec^{4}(x)tan(x) + 2*6sec^{6}(x)tan(x)sec^{4}(tan(x)) + 2sec^{6}(x)*4sec^{4}(tan(x))tan(tan(x))sec^{2}(x)(1) + 4*2tan(tan(x))sec^{2}(tan(x))(sec^{2}(x)(1))sec^{6}(x)sec^{2}(tan(x)) + 4tan^{2}(tan(x))*6sec^{6}(x)tan(x)sec^{2}(tan(x)) + 4tan^{2}(tan(x))sec^{6}(x)*2sec^{2}(tan(x))tan(tan(x))sec^{2}(x)(1)\\=&24tan(x)sec^{6}(x)sec^{4}(tan(x)) + 8tan(tan(x))sec^{8}(x)sec^{4}(tan(x)) + 16tan(x)sec^{4}(x)sec^{2}(tan(x)) + 8tan^{3}(x)sec^{2}(x)sec^{2}(tan(x)) + 56tan^{2}(x)tan(tan(x))sec^{2}(tan(x))sec^{4}(x) + 12tan(tan(x))sec^{6}(x)sec^{2}(tan(x)) + 24tan^{2}(tan(x))tan(x)sec^{6}(x)sec^{2}(tan(x)) + 8tan(tan(x))sec^{4}(tan(x))sec^{8}(x) + 4tan(tan(x))sec^{2}(tan(x))sec^{6}(x) + 24tan(x)tan^{2}(tan(x))sec^{6}(x)sec^{2}(tan(x)) + 8tan^{3}(tan(x))sec^{2}(tan(x))sec^{8}(x)\\ \end{split}\end{equation} \]
注意，变量是区分大小写的。
\[ \begin{equation}\begin{split}【1/5】求函数lg(lg(x)) 关于 x 的 4 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( lg(lg(x))\right)}{dx}\\=&\frac{1}{ln{10}(lg(x))ln{10}(x)}\\=&\frac{1}{xln^{2}{10}lg(x)}\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( \frac{1}{xln^{2}{10}lg(x)}\right)}{dx}\\=&\frac{-1}{x^{2}ln^{2}{10}lg(x)} + \frac{-2*0}{xln^{3}{10}lg(x)} + \frac{-1}{xln^{2}{10}lg^{2}(x)ln{10}(x)}\\=&\frac{-1}{x^{2}ln^{2}{10}lg(x)} - \frac{1}{x^{2}ln^{3}{10}lg^{2}(x)}\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( \frac{-1}{x^{2}ln^{2}{10}lg(x)} - \frac{1}{x^{2}ln^{3}{10}lg^{2}(x)}\right)}{dx}\\=&\frac{--2}{x^{3}ln^{2}{10}lg(x)} - \frac{-2*0}{x^{2}ln^{3}{10}lg(x)} - \frac{-1}{x^{2}ln^{2}{10}lg^{2}(x)ln{10}(x)} - \frac{-2}{x^{3}ln^{3}{10}lg^{2}(x)} - \frac{-3*0}{x^{2}ln^{4}{10}lg^{2}(x)} - \frac{-2}{x^{2}ln^{3}{10}lg^{3}(x)ln{10}(x)}\\=&\frac{2}{x^{3}ln^{2}{10}lg(x)} + \frac{3}{x^{3}ln^{3}{10}lg^{2}(x)} + \frac{2}{x^{3}ln^{4}{10}lg^{3}(x)}\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( \frac{2}{x^{3}ln^{2}{10}lg(x)} + \frac{3}{x^{3}ln^{3}{10}lg^{2}(x)} + \frac{2}{x^{3}ln^{4}{10}lg^{3}(x)}\right)}{dx}\\=&\frac{2*-3}{x^{4}ln^{2}{10}lg(x)} + \frac{2*-2*0}{x^{3}ln^{3}{10}lg(x)} + \frac{2*-1}{x^{3}ln^{2}{10}lg^{2}(x)ln{10}(x)} + \frac{3*-3}{x^{4}ln^{3}{10}lg^{2}(x)} + \frac{3*-3*0}{x^{3}ln^{4}{10}lg^{2}(x)} + \frac{3*-2}{x^{3}ln^{3}{10}lg^{3}(x)ln{10}(x)} + \frac{2*-3}{x^{4}ln^{4}{10}lg^{3}(x)} + \frac{2*-4*0}{x^{3}ln^{5}{10}lg^{3}(x)} + \frac{2*-3}{x^{3}ln^{4}{10}lg^{4}(x)ln{10}(x)}\\=&\frac{-6}{x^{4}ln^{2}{10}lg(x)} - \frac{11}{x^{4}ln^{3}{10}lg^{2}(x)} - \frac{12}{x^{4}ln^{4}{10}lg^{3}(x)} - \frac{6}{x^{4}ln^{5}{10}lg^{4}(x)}\\ \end{split}\end{equation} \]
\[ \begin{equation}\begin{split}【2/5】求函数ln(ln(x)) 关于 x 的 4 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( ln(ln(x))\right)}{dx}\\=&\frac{1}{(ln(x))(x)}\\=&\frac{1}{xln(x)}\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( \frac{1}{xln(x)}\right)}{dx}\\=&\frac{-1}{x^{2}ln(x)} + \frac{-1}{xln^{2}(x)(x)}\\=&\frac{-1}{x^{2}ln(x)} - \frac{1}{x^{2}ln^{2}(x)}\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( \frac{-1}{x^{2}ln(x)} - \frac{1}{x^{2}ln^{2}(x)}\right)}{dx}\\=&\frac{--2}{x^{3}ln(x)} - \frac{-1}{x^{2}ln^{2}(x)(x)} - \frac{-2}{x^{3}ln^{2}(x)} - \frac{-2}{x^{2}ln^{3}(x)(x)}\\=&\frac{2}{x^{3}ln(x)} + \frac{3}{x^{3}ln^{2}(x)} + \frac{2}{x^{3}ln^{3}(x)}\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( \frac{2}{x^{3}ln(x)} + \frac{3}{x^{3}ln^{2}(x)} + \frac{2}{x^{3}ln^{3}(x)}\right)}{dx}\\=&\frac{2*-3}{x^{4}ln(x)} + \frac{2*-1}{x^{3}ln^{2}(x)(x)} + \frac{3*-3}{x^{4}ln^{2}(x)} + \frac{3*-2}{x^{3}ln^{3}(x)(x)} + \frac{2*-3}{x^{4}ln^{3}(x)} + \frac{2*-3}{x^{3}ln^{4}(x)(x)}\\=&\frac{-6}{x^{4}ln(x)} - \frac{11}{x^{4}ln^{2}(x)} - \frac{12}{x^{4}ln^{3}(x)} - \frac{6}{x^{4}ln^{4}(x)}\\ \end{split}\end{equation} \]
\[ \begin{equation}\begin{split}【3/5】求函数sin(sin(x)) 关于 x 的 4 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( sin(sin(x))\right)}{dx}\\=&cos(sin(x))cos(x)\\=&cos(x)cos(sin(x))\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( cos(x)cos(sin(x))\right)}{dx}\\=&-sin(x)cos(sin(x)) + cos(x)*-sin(sin(x))cos(x)\\=&-sin(x)cos(sin(x)) - sin(sin(x))cos^{2}(x)\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( -sin(x)cos(sin(x)) - sin(sin(x))cos^{2}(x)\right)}{dx}\\=&-cos(x)cos(sin(x)) - sin(x)*-sin(sin(x))cos(x) - cos(sin(x))cos(x)cos^{2}(x) - sin(sin(x))*-2cos(x)sin(x)\\=&-cos(x)cos(sin(x)) + 3sin(x)sin(sin(x))cos(x) - cos^{3}(x)cos(sin(x))\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( -cos(x)cos(sin(x)) + 3sin(x)sin(sin(x))cos(x) - cos^{3}(x)cos(sin(x))\right)}{dx}\\=&--sin(x)cos(sin(x)) - cos(x)*-sin(sin(x))cos(x) + 3cos(x)sin(sin(x))cos(x) + 3sin(x)cos(sin(x))cos(x)cos(x) + 3sin(x)sin(sin(x))*-sin(x) - -3cos^{2}(x)sin(x)cos(sin(x)) - cos^{3}(x)*-sin(sin(x))cos(x)\\=&6sin(x)cos^{2}(x)cos(sin(x)) + 4sin(sin(x))cos^{2}(x) - 3sin^{2}(x)sin(sin(x)) + sin(x)cos(sin(x)) + sin(sin(x))cos^{4}(x)\\ \end{split}\end{equation} \]
\[ \begin{equation}\begin{split}【4/5】求函数cos(cos(x)) 关于 x 的 4 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( cos(cos(x))\right)}{dx}\\=&-sin(cos(x))*-sin(x)\\=&sin(x)sin(cos(x))\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( sin(x)sin(cos(x))\right)}{dx}\\=&cos(x)sin(cos(x)) + sin(x)cos(cos(x))*-sin(x)\\=&sin(cos(x))cos(x) - sin^{2}(x)cos(cos(x))\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( sin(cos(x))cos(x) - sin^{2}(x)cos(cos(x))\right)}{dx}\\=&cos(cos(x))*-sin(x)cos(x) + sin(cos(x))*-sin(x) - 2sin(x)cos(x)cos(cos(x)) - sin^{2}(x)*-sin(cos(x))*-sin(x)\\=&-sin(x)cos(cos(x))cos(x) - sin(x)sin(cos(x)) - 2sin(x)cos(x)cos(cos(x)) - sin(cos(x))sin^{3}(x)\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( -sin(x)cos(cos(x))cos(x) - sin(x)sin(cos(x)) - 2sin(x)cos(x)cos(cos(x)) - sin(cos(x))sin^{3}(x)\right)}{dx}\\=&-cos(x)cos(cos(x))cos(x) - sin(x)*-sin(cos(x))*-sin(x)cos(x) - sin(x)cos(cos(x))*-sin(x) - cos(x)sin(cos(x)) - sin(x)cos(cos(x))*-sin(x) - 2cos(x)cos(x)cos(cos(x)) - 2sin(x)*-sin(x)cos(cos(x)) - 2sin(x)cos(x)*-sin(cos(x))*-sin(x) - cos(cos(x))*-sin(x)sin^{3}(x) - sin(cos(x))*3sin^{2}(x)cos(x)\\=&-3cos^{2}(x)cos(cos(x)) - 3sin(cos(x))sin^{2}(x)cos(x) + 4sin^{2}(x)cos(cos(x)) - sin(cos(x))cos(x) + sin^{4}(x)cos(cos(x)) - 3sin^{2}(x)sin(cos(x))cos(x)\\ \end{split}\end{equation} \]
\[ \begin{equation}\begin{split}【5/5】求函数tan(tan(x)) 关于 x 的 4 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( tan(tan(x))\right)}{dx}\\=&sec^{2}(tan(x))(sec^{2}(x)(1))\\=&sec^{2}(x)sec^{2}(tan(x))\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( sec^{2}(x)sec^{2}(tan(x))\right)}{dx}\\=&2sec^{2}(x)tan(x)sec^{2}(tan(x)) + sec^{2}(x)*2sec^{2}(tan(x))tan(tan(x))sec^{2}(x)(1)\\=&2tan(x)sec^{2}(x)sec^{2}(tan(x)) + 2tan(tan(x))sec^{2}(tan(x))sec^{4}(x)\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( 2tan(x)sec^{2}(x)sec^{2}(tan(x)) + 2tan(tan(x))sec^{2}(tan(x))sec^{4}(x)\right)}{dx}\\=&2sec^{2}(x)(1)sec^{2}(x)sec^{2}(tan(x)) + 2tan(x)*2sec^{2}(x)tan(x)sec^{2}(tan(x)) + 2tan(x)sec^{2}(x)*2sec^{2}(tan(x))tan(tan(x))sec^{2}(x)(1) + 2sec^{2}(tan(x))(sec^{2}(x)(1))sec^{2}(tan(x))sec^{4}(x) + 2tan(tan(x))*2sec^{2}(tan(x))tan(tan(x))sec^{2}(x)(1)sec^{4}(x) + 2tan(tan(x))sec^{2}(tan(x))*4sec^{4}(x)tan(x)\\=&2sec^{4}(x)sec^{2}(tan(x)) + 4tan^{2}(x)sec^{2}(x)sec^{2}(tan(x)) + 12tan(x)tan(tan(x))sec^{2}(tan(x))sec^{4}(x) + 2sec^{6}(x)sec^{4}(tan(x)) + 4tan^{2}(tan(x))sec^{6}(x)sec^{2}(tan(x))\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( 2sec^{4}(x)sec^{2}(tan(x)) + 4tan^{2}(x)sec^{2}(x)sec^{2}(tan(x)) + 12tan(x)tan(tan(x))sec^{2}(tan(x))sec^{4}(x) + 2sec^{6}(x)sec^{4}(tan(x)) + 4tan^{2}(tan(x))sec^{6}(x)sec^{2}(tan(x))\right)}{dx}\\=&2*4sec^{4}(x)tan(x)sec^{2}(tan(x)) + 2sec^{4}(x)*2sec^{2}(tan(x))tan(tan(x))sec^{2}(x)(1) + 4*2tan(x)sec^{2}(x)(1)sec^{2}(x)sec^{2}(tan(x)) + 4tan^{2}(x)*2sec^{2}(x)tan(x)sec^{2}(tan(x)) + 4tan^{2}(x)sec^{2}(x)*2sec^{2}(tan(x))tan(tan(x))sec^{2}(x)(1) + 12sec^{2}(x)(1)tan(tan(x))sec^{2}(tan(x))sec^{4}(x) + 12tan(x)sec^{2}(tan(x))(sec^{2}(x)(1))sec^{2}(tan(x))sec^{4}(x) + 12tan(x)tan(tan(x))*2sec^{2}(tan(x))tan(tan(x))sec^{2}(x)(1)sec^{4}(x) + 12tan(x)tan(tan(x))sec^{2}(tan(x))*4sec^{4}(x)tan(x) + 2*6sec^{6}(x)tan(x)sec^{4}(tan(x)) + 2sec^{6}(x)*4sec^{4}(tan(x))tan(tan(x))sec^{2}(x)(1) + 4*2tan(tan(x))sec^{2}(tan(x))(sec^{2}(x)(1))sec^{6}(x)sec^{2}(tan(x)) + 4tan^{2}(tan(x))*6sec^{6}(x)tan(x)sec^{2}(tan(x)) + 4tan^{2}(tan(x))sec^{6}(x)*2sec^{2}(tan(x))tan(tan(x))sec^{2}(x)(1)\\=&24tan(x)sec^{6}(x)sec^{4}(tan(x)) + 8tan(tan(x))sec^{8}(x)sec^{4}(tan(x)) + 16tan(x)sec^{4}(x)sec^{2}(tan(x)) + 8tan^{3}(x)sec^{2}(x)sec^{2}(tan(x)) + 56tan^{2}(x)tan(tan(x))sec^{2}(tan(x))sec^{4}(x) + 12tan(tan(x))sec^{6}(x)sec^{2}(tan(x)) + 24tan^{2}(tan(x))tan(x)sec^{6}(x)sec^{2}(tan(x)) + 8tan(tan(x))sec^{4}(tan(x))sec^{8}(x) + 4tan(tan(x))sec^{2}(tan(x))sec^{6}(x) + 24tan(x)tan^{2}(tan(x))sec^{6}(x)sec^{2}(tan(x)) + 8tan^{3}(tan(x))sec^{2}(tan(x))sec^{8}(x)\\ \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。