There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ \frac{(2 - cos(x))e^{1}}{3} - 1 - (\frac{1}{6})xe^{2}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = - \frac{1}{3}e^{1}cos(x) + \frac{2}{3}e^{1} - \frac{1}{6}xe^{2} - 1\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( - \frac{1}{3}e^{1}cos(x) + \frac{2}{3}e^{1} - \frac{1}{6}xe^{2} - 1\right)}{dx}\\=& - \frac{1}{3}e^{1}*0cos(x) - \frac{1}{3}e^{1}*-sin(x) + \frac{2}{3}e^{1}*0 - \frac{1}{6}e^{2} - \frac{1}{6}xe^{2}*0 + 0\\=&\frac{e^{1}sin(x)}{3} - \frac{e^{2}}{6}\\ \end{split}\end{equation} \]

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