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

Your problem has not been solved here? Please take a look at the  hot problems ！