This video explains how to find higher order derivatives using Faa di Bruno's Formula. Faa di Bruno's formula is a generalization of the chain rule for higher derivatives. It shows you how to find the nth derivative of a function composed with another function, like f(g(x)). This beautiful piece of mathematics combines elements of combinatorics (integer partitions and partitions of sets) with differential calculus.
As a prerequisite to this video, you should know how to apply the product and chain rules of differentiation in calculus, as Faa di Bruno's formula is a generalization of the chain rule.
If you want to learn more about partitions of sets, I suggest you check out my Stirling Numbers of the 2nd Kind video, which covers the ways to partition a set of n elements into non-empty subsets:
https://youtu.be/hKYc9mwPJBA
For more information on Faa di Bruno's formula, check out these links:
1. https://en.wikipedia.org/wiki/Fa%C3%A0_di_Bruno%27s_formula
2. https://mathworld.wolfram.com/FaadiBrunosFormula.html
3. https://www.maa.org/sites/default/files/pdf/upload_library/22/Ford/Johnson217-234.pdf
Thanks for watching!
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#calculus
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