本次共计算 1 个题目：每一题对 x 求 2 阶导数。
    注意，变量是区分大小写的。
\[ \begin{equation}\begin{split}【1/1】求函数x + \frac{arccot(x)}{ln(1 + {x}^{2})} 关于 x 的 2 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = x + \frac{arccot(x)}{ln(x^{2} + 1)}\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( x + \frac{arccot(x)}{ln(x^{2} + 1)}\right)}{dx}\\=&1 + \frac{-(2x + 0)arccot(x)}{ln^{2}(x^{2} + 1)(x^{2} + 1)} + \frac{(\frac{(1)}{(1 + (x)^{2})})}{ln(x^{2} + 1)}\\=&\frac{-2xarccot(x)}{(x^{2} + 1)ln^{2}(x^{2} + 1)} + \frac{1}{(x^{2} + 1)ln(x^{2} + 1)} + 1\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( \frac{-2xarccot(x)}{(x^{2} + 1)ln^{2}(x^{2} + 1)} + \frac{1}{(x^{2} + 1)ln(x^{2} + 1)} + 1\right)}{dx}\\=&\frac{-2(\frac{-(2x + 0)}{(x^{2} + 1)^{2}})xarccot(x)}{ln^{2}(x^{2} + 1)} - \frac{2arccot(x)}{(x^{2} + 1)ln^{2}(x^{2} + 1)} - \frac{2x*-2(2x + 0)arccot(x)}{(x^{2} + 1)ln^{3}(x^{2} + 1)(x^{2} + 1)} - \frac{2x(\frac{(1)}{(1 + (x)^{2})})}{(x^{2} + 1)ln^{2}(x^{2} + 1)} + \frac{(\frac{-(2x + 0)}{(x^{2} + 1)^{2}})}{ln(x^{2} + 1)} + \frac{-(2x + 0)}{(x^{2} + 1)ln^{2}(x^{2} + 1)(x^{2} + 1)} + 0\\=&\frac{4x^{2}arccot(x)}{(x^{2} + 1)^{2}ln^{2}(x^{2} + 1)} - \frac{2arccot(x)}{(x^{2} + 1)ln^{2}(x^{2} + 1)} + \frac{8x^{2}arccot(x)}{(x^{2} + 1)^{2}ln^{3}(x^{2} + 1)} - \frac{4x}{(x^{2} + 1)^{2}ln^{2}(x^{2} + 1)} - \frac{2x}{(x^{2} + 1)^{2}ln(x^{2} + 1)}\\ \end{split}\end{equation} \]

你的问题在这里没有得到解决？请到 热门难题 里面看看吧！