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

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