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

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