There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ {\frac{1}{2}}^{x}cos({3}^{x}πx)\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = {\frac{1}{2}}^{x}cos(πx{3}^{x})\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( {\frac{1}{2}}^{x}cos(πx{3}^{x})\right)}{dx}\\=&({\frac{1}{2}}^{x}((1)ln(\frac{1}{2}) + \frac{(x)(0)}{(\frac{1}{2})}))cos(πx{3}^{x}) + {\frac{1}{2}}^{x}*-sin(πx{3}^{x})(π{3}^{x} + πx({3}^{x}((1)ln(3) + \frac{(x)(0)}{(3)})))\\=&{\frac{1}{2}}^{x}ln(\frac{1}{2})cos(πx{3}^{x}) - π{\frac{1}{2}}^{(2x)}sin(πx{3}^{x}) - πx{3}^{(2x)}ln(3)sin(πx{3}^{x})\\ \end{split}\end{equation} \]

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