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

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