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

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