There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ {{e}^{(3x)}}^{(log*8((3{x}^{2}) - (\frac{1}{x}) + ({2}^{x})))}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = {{e}^{(3x)}}^{(24logx^{2} - \frac{8log}{x} + 8log{2}^{x})}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( {{e}^{(3x)}}^{(24logx^{2} - \frac{8log}{x} + 8log{2}^{x})}\right)}{dx}\\=&({{e}^{(3x)}}^{(24logx^{2} - \frac{8log}{x} + 8log{2}^{x})}((24log*2x - \frac{8log*-1}{x^{2}} + 8log({2}^{x}((1)ln(2) + \frac{(x)(0)}{(2)})))ln({e}^{(3x)}) + \frac{(24logx^{2} - \frac{8log}{x} + 8log{2}^{x})(({e}^{(3x)}((3)ln(e) + \frac{(3x)(0)}{(e)})))}{({e}^{(3x)})}))\\=&48logx{{e}^{(3x)}}^{(24logx^{2} - \frac{8log}{x} + 8log{2}^{x})}ln({e}^{(3x)}) + \frac{8log{{e}^{(3x)}}^{(24logx^{2} - \frac{8log}{x} + 8log{2}^{x})}ln({e}^{(3x)})}{x^{2}} + 8log{2}^{x}{{e}^{(3x)}}^{(24logx^{2} - \frac{8log}{x} + 8log{2}^{x})}ln({e}^{(3x)})ln(2) + 72logx^{2}{{e}^{(3x)}}^{(24logx^{2} - \frac{8log}{x} + 8log{2}^{x})} - \frac{24log{{e}^{(3x)}}^{(24logx^{2} - \frac{8log}{x} + 8log{2}^{x})}}{x} + 24log{2}^{x}{{e}^{(3x)}}^{(24logx^{2} - \frac{8log}{x} + 8log{2}^{x})}\\ \end{split}\end{equation} \]

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