# Zero solvers challenge

Calculus Level 5

$\large f(x) = x^4 e^{x}$

If the $$100^\text{th}$$ derivative of $$f(x)$$ at $$x=1$$ is equal to $$k e$$ for some positive integer $$k$$, find $$k$$.

Notation: $$e \approx 2.71828$$ denotes the Euler's number.

Part 2

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