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

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