Evaluate

\[\left[ \left.\frac{d^{\pi}}{dx^{\pi}}\right|_{x=\phi}(x^{e}) \right].\]

**Details and Assumptions**

\([x]\) is the nearest integer function.

\(\phi=\frac{1+\sqrt{5}}{2}.\)

\(e=\displaystyle \lim_{n \rightarrow \infty}{\left ( 1+\frac{1}{n} \right )^n}.\)

\(\displaystyle{\pi=2 \int_{0}^{\infty}{\frac{1}{1+x^2}dx}}.\)

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