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

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