There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ (\frac{(x + 5)}{2}){(\frac{1}{2})}^{(x + 1)}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{1}{2}x{\frac{1}{2}}^{(x + 1)} + \frac{5}{2} * {\frac{1}{2}}^{(x + 1)}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{1}{2}x{\frac{1}{2}}^{(x + 1)} + \frac{5}{2} * {\frac{1}{2}}^{(x + 1)}\right)}{dx}\\=&\frac{1}{2} * {\frac{1}{2}}^{(x + 1)} + \frac{1}{2}x({\frac{1}{2}}^{(x + 1)}((1 + 0)ln(\frac{1}{2}) + \frac{(x + 1)(0)}{(\frac{1}{2})})) + \frac{5}{2}({\frac{1}{2}}^{(x + 1)}((1 + 0)ln(\frac{1}{2}) + \frac{(x + 1)(0)}{(\frac{1}{2})}))\\=&\frac{5 * {\frac{1}{2}}^{(x + 1)}ln(\frac{1}{2})}{2} + \frac{x{\frac{1}{2}}^{(x + 1)}ln(\frac{1}{2})}{2} + \frac{{\frac{1}{2}}^{(x + 1)}}{2}\\ \end{split}\end{equation} \]

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