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

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