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

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