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

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