There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ ({e}^{{x}^{2}} + {e}^{({x}^{2} + 1)})ln({e}^{{x}^{2}} + {e}^{({x}^{2} + 1)})\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = {e}^{x^{2}}ln({e}^{x^{2}} + {e}^{(x^{2} + 1)}) + {e}^{(x^{2} + 1)}ln({e}^{x^{2}} + {e}^{(x^{2} + 1)})\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( {e}^{x^{2}}ln({e}^{x^{2}} + {e}^{(x^{2} + 1)}) + {e}^{(x^{2} + 1)}ln({e}^{x^{2}} + {e}^{(x^{2} + 1)})\right)}{dx}\\=&({e}^{x^{2}}((2x)ln(e) + \frac{(x^{2})(0)}{(e)}))ln({e}^{x^{2}} + {e}^{(x^{2} + 1)}) + \frac{{e}^{x^{2}}(({e}^{x^{2}}((2x)ln(e) + \frac{(x^{2})(0)}{(e)})) + ({e}^{(x^{2} + 1)}((2x + 0)ln(e) + \frac{(x^{2} + 1)(0)}{(e)})))}{({e}^{x^{2}} + {e}^{(x^{2} + 1)})} + ({e}^{(x^{2} + 1)}((2x + 0)ln(e) + \frac{(x^{2} + 1)(0)}{(e)}))ln({e}^{x^{2}} + {e}^{(x^{2} + 1)}) + \frac{{e}^{(x^{2} + 1)}(({e}^{x^{2}}((2x)ln(e) + \frac{(x^{2})(0)}{(e)})) + ({e}^{(x^{2} + 1)}((2x + 0)ln(e) + \frac{(x^{2} + 1)(0)}{(e)})))}{({e}^{x^{2}} + {e}^{(x^{2} + 1)})}\\=&2x{e}^{x^{2}}ln({e}^{x^{2}} + {e}^{(x^{2} + 1)}) + \frac{4x{e}^{(2x^{2} + 2)}}{({e}^{x^{2}} + {e}^{(x^{2} + 1)})} + 2x{e}^{(x^{2} + 1)}ln({e}^{x^{2}} + {e}^{(x^{2} + 1)}) + \frac{4x{e}^{(2x^{2})}}{({e}^{x^{2}} + {e}^{(x^{2} + 1)})}\\ \end{split}\end{equation} \]

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