Derivative function：
Enter an original function (that is, the function to be derived), then set the variable to be derived and the order of the derivative, and click the "Next" button to obtain the derivative function of the corresponding order of the function.
Note that the input function supports mathematical functions and other constants.
Enter an original function (that is, the function to be derived), then set the variable to be derived and the order of the derivative, and click the "Next" button to obtain the derivative function of the corresponding order of the function.
Note that the input function supports mathematical functions and other constants.
Current location：Derivative function > Derivative function calculation history > Answer
There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}\right)}{dx}\\=&e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^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\end{split}\end{equation} \]
Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}\right)}{dx}\\=&e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^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\end{split}\end{equation} \]