There are 1 questions in this calculation: for each question, the 2 derivative of t is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ second\ derivative\ of\ function\ ln(t + {({t}^{2} + 1)}^{\frac{1}{2}})\ with\ respect\ to\ t：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = ln(t + (t^{2} + 1)^{\frac{1}{2}})\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( ln(t + (t^{2} + 1)^{\frac{1}{2}})\right)}{dt}\\=&\frac{(1 + (\frac{\frac{1}{2}(2t + 0)}{(t^{2} + 1)^{\frac{1}{2}}}))}{(t + (t^{2} + 1)^{\frac{1}{2}})}\\=&\frac{t}{(t + (t^{2} + 1)^{\frac{1}{2}})(t^{2} + 1)^{\frac{1}{2}}} + \frac{1}{(t + (t^{2} + 1)^{\frac{1}{2}})}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{t}{(t + (t^{2} + 1)^{\frac{1}{2}})(t^{2} + 1)^{\frac{1}{2}}} + \frac{1}{(t + (t^{2} + 1)^{\frac{1}{2}})}\right)}{dt}\\=&\frac{(\frac{-(1 + (\frac{\frac{1}{2}(2t + 0)}{(t^{2} + 1)^{\frac{1}{2}}}))}{(t + (t^{2} + 1)^{\frac{1}{2}})^{2}})t}{(t^{2} + 1)^{\frac{1}{2}}} + \frac{(\frac{\frac{-1}{2}(2t + 0)}{(t^{2} + 1)^{\frac{3}{2}}})t}{(t + (t^{2} + 1)^{\frac{1}{2}})} + \frac{1}{(t + (t^{2} + 1)^{\frac{1}{2}})(t^{2} + 1)^{\frac{1}{2}}} + (\frac{-(1 + (\frac{\frac{1}{2}(2t + 0)}{(t^{2} + 1)^{\frac{1}{2}}}))}{(t + (t^{2} + 1)^{\frac{1}{2}})^{2}})\\=& - \frac{t^{2}}{(t + (t^{2} + 1)^{\frac{1}{2}})^{2}(t^{2} + 1)} - \frac{2t}{(t + (t^{2} + 1)^{\frac{1}{2}})^{2}(t^{2} + 1)^{\frac{1}{2}}} - \frac{t^{2}}{(t + (t^{2} + 1)^{\frac{1}{2}})(t^{2} + 1)^{\frac{3}{2}}} + \frac{1}{(t + (t^{2} + 1)^{\frac{1}{2}})(t^{2} + 1)^{\frac{1}{2}}} - \frac{1}{(t + (t^{2} + 1)^{\frac{1}{2}})^{2}}\\ \end{split}\end{equation} \]

Your problem has not been solved here? Please take a look at the  hot problems ！