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

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