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

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