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

你的问题在这里没有得到解决？请到 热门难题 里面看看吧！