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

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