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。
\[ \begin{equation}\begin{split}【1/1】求函数(sqrt(2) - 1.41421)lg(x) 关于 x 的 4 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = lg(x)sqrt(2) - 1.41421lg(x)\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( lg(x)sqrt(2) - 1.41421lg(x)\right)}{dx}\\=&\frac{sqrt(2)}{ln{10}(x)} + lg(x)*0*0.5*2^{\frac{1}{2}} - \frac{1.41421}{ln{10}(x)}\\=&\frac{sqrt(2)}{xln{10}} - \frac{1.41421}{xln{10}}\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( \frac{sqrt(2)}{xln{10}} - \frac{1.41421}{xln{10}}\right)}{dx}\\=&\frac{-sqrt(2)}{x^{2}ln{10}} + \frac{-*0sqrt(2)}{xln^{2}{10}} + \frac{*0*0.5*2^{\frac{1}{2}}}{xln{10}} - \frac{1.41421*-1}{x^{2}ln{10}} - \frac{1.41421*-0}{xln^{2}{10}}\\=&\frac{-sqrt(2)}{x^{2}ln{10}} + \frac{1.41421}{x^{2}ln{10}}\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( \frac{-sqrt(2)}{x^{2}ln{10}} + \frac{1.41421}{x^{2}ln{10}}\right)}{dx}\\=&\frac{-*-2sqrt(2)}{x^{3}ln{10}} - \frac{-*0sqrt(2)}{x^{2}ln^{2}{10}} - \frac{*0*0.5*2^{\frac{1}{2}}}{x^{2}ln{10}} + \frac{1.41421*-2}{x^{3}ln{10}} + \frac{1.41421*-0}{x^{2}ln^{2}{10}}\\=&\frac{2sqrt(2)}{x^{3}ln{10}} - \frac{2.82842}{x^{3}ln{10}}\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( \frac{2sqrt(2)}{x^{3}ln{10}} - \frac{2.82842}{x^{3}ln{10}}\right)}{dx}\\=&\frac{2*-3sqrt(2)}{x^{4}ln{10}} + \frac{2*-*0sqrt(2)}{x^{3}ln^{2}{10}} + \frac{2*0*0.5*2^{\frac{1}{2}}}{x^{3}ln{10}} - \frac{2.82842*-3}{x^{4}ln{10}} - \frac{2.82842*-0}{x^{3}ln^{2}{10}}\\=&\frac{-6sqrt(2)}{x^{4}ln{10}} + \frac{8.48526}{x^{4}ln{10}}\\ \end{split}\end{equation} \]

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