Whoa! Extreme!

Calculus Level 2

\[f(x) = \frac{x^{10^{100}} + x^{10^{100} - 1} + x^{10^{100} - 2} + x^{10^{100} - 3} ... + x^1}{(\pi e \pi e \pi e \pi e \pi)^{-1} (10^{100})!}\]

What's the googol'th derivative of \(f(x)\) ?

Details and assumptions:

  • \(googol = 10^{100}\)
  • Round to the nearest tenth.
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