# I Higher order derivatives rules

1. Oct 26, 2017

### LauwranceGilbert

mod: moved from homework

Does anyone know why and when this equation holds? I have searched online but cannot find the reason or the rules for the higher order derivatives.

Last edited by a moderator: Oct 26, 2017
2. Oct 26, 2017

### Staff: Mentor

Can you provide some context of where you found this equation and what you were investigating?

It looks like ordinary power rules applied to derivatives ie derivative chain rule.

https://en.wikipedia.org/wiki/Chain_rule

There's a section further into the article talking about generalizations of the rule:

Here's a presentation where they use something like this for trig derivatives:

https://www.cs.drexel.edu/classes/Calculus/MATH121_Fall02/lecture14.pdf

Last edited: Oct 26, 2017
3. Oct 26, 2017

### Ray Vickson

The first equality is easy: the $(4M+4)$th derivative of $F$ is just the 4th derivative of the $(4M)$th derivative. The second equality is false, in general, because there are many counterexamples. The $(4M+4)$th derivative is usually not a constant ($= (-4)^M$ ) times the 4th derivative.