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

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