# Zero solvers challenge 2

Calculus Level 5

$\large f(x) = \dfrac{e^{x}}{x^3}$

If the $100^\text{th}$ derivative of $f(x)$ at $x=1$ is equal to $\dfrac{ke}{2}$ for some integer $k$, find $k$.

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

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