Interesting Successive Differentiation Formula

Hello, I would like to share this video on Faa di Bruno's formula, a formula that generalizes the chain rule to higher-order derivatives. What's so interesting about it is the connections to integer partitions and discrete math. Hope you like it:

ooh nice btw the generalization of product rule is called Leibniz's differentiation rule

hm... how can we prove that for all n, the n-tuple (m_1, m_2, ..., m_n) exists such that $\sum_{i=1}^n i \cdot m_i = n !$?

Thanks! I might do a video on that rule sometime.