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

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