# Vieta's Derivative II -- My 500-follower problem

Calculus Level 4

The function $$x^5 + 6x^4 - 18x^3 -10x^2 + 45x -24$$ has only four distinct real roots: $$\alpha$$, $$\beta$$, $$\gamma$$ and $$\delta$$ (in no particular order). If $$f'(x)$$ is the first derivative of $$f(x)$$. Evaluate

$f'(\alpha) + f'(\beta) + f'(\gamma) + f'(\delta)$

Inspiration: This is exactly the problem titled Inspired by Vieta's Derivatives with a twist.

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