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

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