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

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