There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ \frac{{(3 + x)}^{(x + 1)}}{2}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{1}{2}(x + 3)^{(x + 1)}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{1}{2}(x + 3)^{(x + 1)}\right)}{dx}\\=&\frac{1}{2}((x + 3)^{(x + 1)}((1 + 0)ln(x + 3) + \frac{(x + 1)(1 + 0)}{(x + 3)}))\\=&\frac{(x + 3)^{(x + 1)}ln(x + 3)}{2} + \frac{x(x + 3)^{(x + 1)}}{2(x + 3)} + \frac{(x + 3)^{(x + 1)}}{2(x + 3)}\\ \end{split}\end{equation} \]

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