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

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