There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ lg(x) + sqrt({x}^{2} - x - 2) + {e}^{x} + {2}^{x} + sin(x) + cos(x) + tan(x) + {x}^{e}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = lg(x) + sqrt(x^{2} - x - 2) + {e}^{x} + {2}^{x} + sin(x) + cos(x) + tan(x) + {x}^{e}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( lg(x) + sqrt(x^{2} - x - 2) + {e}^{x} + {2}^{x} + sin(x) + cos(x) + tan(x) + {x}^{e}\right)}{dx}\\=&\frac{1}{ln{10}(x)} + \frac{(2x - 1 + 0)*\frac{1}{2}}{(x^{2} - x - 2)^{\frac{1}{2}}} + ({e}^{x}((1)ln(e) + \frac{(x)(0)}{(e)})) + ({2}^{x}((1)ln(2) + \frac{(x)(0)}{(2)})) + cos(x) + -sin(x) + sec^{2}(x)(1) + ({x}^{e}((0)ln(x) + \frac{(e)(1)}{(x)}))\\=&\frac{1}{xln{10}} + \frac{x}{(x^{2} - x - 2)^{\frac{1}{2}}} - \frac{1}{2(x^{2} - x - 2)^{\frac{1}{2}}} + {2}^{x}ln(2) + \frac{{x}^{e}e}{x} + cos(x) - sin(x) + sec^{2}(x) + {e}^{x}\\ \end{split}\end{equation} \]

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