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。
\[ \begin{equation}\begin{split}【1/1】求函数 - lg(cos(x)) 关于 x 的 4 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( - lg(cos(x))\right)}{dx}\\=& - \frac{-sin(x)}{ln{10}(cos(x))}\\=&\frac{sin(x)}{ln{10}cos(x)}\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( \frac{sin(x)}{ln{10}cos(x)}\right)}{dx}\\=&\frac{-0sin(x)}{ln^{2}{10}cos(x)} + \frac{cos(x)}{ln{10}cos(x)} + \frac{sin(x)sin(x)}{ln{10}cos^{2}(x)}\\=&\frac{sin^{2}(x)}{ln{10}cos^{2}(x)} + \frac{1}{ln{10}}\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( \frac{sin^{2}(x)}{ln{10}cos^{2}(x)} + \frac{1}{ln{10}}\right)}{dx}\\=&\frac{-0sin^{2}(x)}{ln^{2}{10}cos^{2}(x)} + \frac{2sin(x)cos(x)}{ln{10}cos^{2}(x)} + \frac{sin^{2}(x)*2sin(x)}{ln{10}cos^{3}(x)} + \frac{-0}{ln^{2}{10}}\\=&\frac{2sin(x)}{ln{10}cos(x)} + \frac{2sin^{3}(x)}{ln{10}cos^{3}(x)}\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( \frac{2sin(x)}{ln{10}cos(x)} + \frac{2sin^{3}(x)}{ln{10}cos^{3}(x)}\right)}{dx}\\=&\frac{2*-0sin(x)}{ln^{2}{10}cos(x)} + \frac{2cos(x)}{ln{10}cos(x)} + \frac{2sin(x)sin(x)}{ln{10}cos^{2}(x)} + \frac{2*-0sin^{3}(x)}{ln^{2}{10}cos^{3}(x)} + \frac{2*3sin^{2}(x)cos(x)}{ln{10}cos^{3}(x)} + \frac{2sin^{3}(x)*3sin(x)}{ln{10}cos^{4}(x)}\\=&\frac{8sin^{2}(x)}{ln{10}cos^{2}(x)} + \frac{6sin^{4}(x)}{ln{10}cos^{4}(x)} + \frac{2}{ln{10}}\\ \end{split}\end{equation} \]

你的问题在这里没有得到解决？请到 热门难题 里面看看吧！