There are 1 questions in this calculation: for each question, the 2 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ second\ derivative\ of\ function\ ln(x + \frac{{(x + 1)}^{1}}{2})\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = ln(\frac{3}{2}x + \frac{1}{2})\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( ln(\frac{3}{2}x + \frac{1}{2})\right)}{dx}\\=&\frac{(\frac{3}{2} + 0)}{(\frac{3}{2}x + \frac{1}{2})}\\=&\frac{3}{2(\frac{3}{2}x + \frac{1}{2})}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{3}{2(\frac{3}{2}x + \frac{1}{2})}\right)}{dx}\\=&\frac{3(\frac{-(\frac{3}{2} + 0)}{(\frac{3}{2}x + \frac{1}{2})^{2}})}{2}\\=&\frac{-9}{4(\frac{3}{2}x + \frac{1}{2})^{2}}\\ \end{split}\end{equation} \]

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