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

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