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

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