There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ {({e}^{a})}^{x}ln({e}^{a})sin(2x) + 2{({e}^{a})}^{x}cos(2x) - 2a\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = a{{e}^{a}}^{x}sin(2x) + 2{{e}^{a}}^{x}cos(2x) - 2a\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( a{{e}^{a}}^{x}sin(2x) + 2{{e}^{a}}^{x}cos(2x) - 2a\right)}{dx}\\=&a({{e}^{a}}^{x}((1)ln({e}^{a}) + \frac{(x)(({e}^{a}((0)ln(e) + \frac{(a)(0)}{(e)})))}{({e}^{a})}))sin(2x) + a{{e}^{a}}^{x}cos(2x)*2 + 2({{e}^{a}}^{x}((1)ln({e}^{a}) + \frac{(x)(({e}^{a}((0)ln(e) + \frac{(a)(0)}{(e)})))}{({e}^{a})}))cos(2x) + 2{{e}^{a}}^{x}*-sin(2x)*2 + 0\\=&a{{e}^{a}}^{x}ln({e}^{a})sin(2x) + 2a{{e}^{a}}^{x}cos(2x) + 2{{e}^{a}}^{x}ln({e}^{a})cos(2x) - 4{{e}^{a}}^{x}sin(2x)\\ \end{split}\end{equation} \]

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