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

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